A391647 - OEIS

A391647

G.f. A(x) satisfies A(x) = 1/(1 - x/(1 - x*A(x)^2)^4).

1, 1, 5, 27, 169, 1142, 8119, 59858, 453457, 3508387, 27605438, 220222006, 1777070719, 14479635755, 118964104210, 984458054901, 8198036158377, 68648565704822, 577688470851287, 4882818680082470, 41435273356227698, 352880834583149468, 3015103372002933094

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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)^4), where B(x) is the g.f. of A391650.

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

MATHEMATICA

Table[Sum[Binomial[2*n-k+1, k]*Binomial[n+3*k-1, n-k]/(2*n-k+1), {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Dec 19 2025 *)

PROG

(PARI) a(n, s=4, t=1, u=2) = 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));