Number of Catalan (Cattleya)

Source: Internet
Author: User

Formula:

n <= 2 o'clock, f (n) = n;

n > 2 o'clock, f (n) = (4n-2)/(n+1) * F (n-1)


The Cattleya list of 1-100 is as follows:

n f (N)

1 12 23 54 145 426 1327 4298 14309 486210 1679611 5878612 20801213 74290014 267444015 969484516 3535767017 12964479018 47763870019 176726319      020 656412042021 2446626702022 9148256364023 34305961365024 128990414732425 486194640145226 1836735307215227 6953355091600428 26374795175036029 100224221665136830 381498650209230431 14      54463603922690932 5553406487704819833 21233613041224311034) 81294404214973076435 311628549490730126236 1195979838586045349237 4595080432462174236438 17673386278700670140039) 68042537172997580039040 262 212704227649210882041 1011391859163789813402042 3904442991190444395924043) 15085347920508535166070044 5 8330011959299669308804045 225711785407724807325372046 874032871153317339004632047 3386877375719104688642949 048 13132789824216936547799190049 50955224517961713805460857250 197826165775616065362377445651 768478567051431638523081615652 2986916694577262595014241751253 11615787145578243425055384588054 45195971802795347144760950942455 1759 41461660881887099247987597256 685245692784487349754965846431257 2670095285677485190424522091266458 10408846 028912230403349831881208059 40594499512757698573064344336711260 158385096459612004268677277903889661 618212      795858485565048708084721633662 2413973774304562682571145854627331263 9429585055877197978793538494638012564 36847916987581665947900904271354695065 144041857315091966887248989424386535066 563268158456031273499391570584914 510067 2203372502195651746335855261405694995068 8621892399896028572618564066370110850069 337485502510215975      55678379345505862470070 132142210842028227048994217719022954460071 517556992464610555941894019399506571635072 2027689038970939986292899856825464102570073 7946348936507737784120823763234926888450074 31149687831110332113753629151880913402724075 122139565443037881182876072200796213079102076 479040893036330391132838620839486446102452077 187931427268098 8457521136127908754519325004078 7374524361153245845969015185464732923933560079 289450081175264899454283846029490       76726439223080 113635957794733627193163287700466745666761394081 446229004998832048246324129750613318349965474082 1752658501561677683473514051791565563639623428083 6885444113278019470788805203466864714298520610084 270557 45103939511802864246328916856642067128044085 106335370292227383597303665804347645872310340452086 418008007355652 473451469582817090745842875131432087 1643531483466542679706914496076288614336759039494088 6463326058576291437049 663748614618146268153526100089 25422415830400079652395344077884164708654737202660090 100013460080035478192939925 053654186436246108995080091 393531223358400468541785357276334950977403168002380092 15487357822491889407128326963778343232013931127835600 93 6096087653534041575146256358082964889196972890743800094 23999334551807700516891577662347672300628082748822960 095 94497379797742820785260587045493959683723075823490405096 372144320440595438556387054137924665970950669737869 430097 1465792935612957543701687784665703276171295495089975510098 5774335806960135778218770060804285633402073162 475661100099 227508830794229349661819540395688853956041682601541047340100 89651994709013149668717007007410063242 0837521538745909320

Number of Catalan (Cattleya)

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