A391649 - OEIS

A391649

G.f. A(x) satisfies A(x) = 1/(1 - x/(1 - x*A(x)^3)^2).

1, 1, 3, 14, 75, 438, 2704, 17356, 114661, 774514, 5324812, 37137379, 262112002, 1868610856, 13436074970, 97328988039, 709609323325, 5203171782012, 38345109874752, 283864224950635, 2109947626538162, 15740670860816827, 117819995601231131, 884569446129847355

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OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: 1/(1 - x*B(x)^2), where B(x) is the g.f. of A367239.

a(n) = Sum_{k=0..n} binomial(3*n-2*k+1,k) * binomial(n+k-1,n-k)/(3*n-2*k+1).

MATHEMATICA

Table[Sum[Binomial[3*n-2*k+1, k]*Binomial[n+k-1, n-k]/(3*n-2*k+1), {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Dec 20 2025 *)

PROG

(PARI) a(n, s=2, t=1, u=3) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));