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A023421 Generalized Catalan Numbers. 5
1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 65, 133, 274, 568, 1184, 2481, 5223, 11042, 23434, 49908, 106633, 228505, 490999, 1057683, 2283701, 4941502, 10713941, 23272929, 50642017, 110377543, 240944076, 526717211, 1152996206, 2527166334, 5545804784, 12184053993 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..2795

FORMULA

G.f. A(x) satisfies: A(x) = (1 + x^2 * A(x)^2) / (1 - x + x^2 + x^3 + x^4). - Ilya Gutkovskiy, Jul 20 2021

MAPLE

A023421 := proc(n)

option remember;

if n = 0 then

1;

else

procname(n-1)+add(procname(k)*procname(n-2-k), k=3..n-2) ;

end if;

end proc: # R. J. Mathar, May 01 2015

MATHEMATICA

a[0]=1; a[n_]:= a[n]=a[n-1] + Sum[a[k]*a[n-2-k], {k, 3, n-2}]; Table[a[n], {n, 0, 30}] (* modified by G. C. Greubel, Jan 01 2018 *)

PROG

(PARI) {a(n) = if(n==0, 1, a(n-1) + sum(k=3, n-2, a(k)*a(n-k-2)))};

for(n=0, 30, print1(a(n), ", ")) \\ G. C. Greubel, Jan 01 2018

CROSSREFS

Cf. A000108, A001006, A004148, A004149, A023422, A023423.

Fourth row of A064645.

Sequence in context: A264701 A195904 A101333 * A098051 A329053 A084637

Adjacent sequences: A023418 A023419 A023420 * A023422 A023423 A023424

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified December 5 06:35 EST 2022. Contains 358582 sequences. (Running on oeis4.)