A387675 Expansion of g/(1 + x^2*g), where g = 1+x*g^3 is the g.f. of A001764.

1, 1, 2, 10, 49, 246, 1296, 7075, 39643, 226702, 1317861, 7764889, 46268870, 278346596, 1688259419, 10312826475, 63389602420, 391781401090, 2433274627913, 15178800798949, 95059061633335, 597443640806208, 3767102249869664, 23823350764759488, 151069360680351577

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{k=0..floor(n/2)} (-1)^k * (k+1) * binomial(3*n-5*k+1,n-2*k)/(3*n-5*k+1).

Prog

(PARI) a(n) = sum(k=0, n\2, (-1)^k*(k+1)*binomial(3*n-5*k+1, n-2*k)/(3*n-5*k+1));

Crossrefs

Cf. A023053, A387676.

Cf. A001764, A391058.

Sequence in context: A330543 A052576 A279852 * A219662 A355153 A268108

Adjacent sequences: A387672 A387673 A387674 * A387676 A387677 A387678

Keyword

nonn

Author

Seiichi Manyama, Nov 30 2025

Status

approved