A023421 Generalized Catalan Numbers.

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

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: A195904 A101333 A367652 * A098051 A329053 A084637

Adjacent sequences: A023418 A023419 A023420 * A023422 A023423 A023424

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved