A391378 Expansion of g^2/(1 + x*g), where g = 1+x*g^4 is the g.f. of A002293.

1, 1, 7, 40, 267, 1897, 14123, 108719, 858421, 6913914, 56583401, 469200322, 3933669482, 33287843079, 283956543780, 2439153154289, 21080183230758, 183168147509467, 1599221574473345, 14022758576502463, 123435372854088656, 1090356552158960402

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = Sum_{k=0..n} (-1)^k * (k+2) * binomial(4*n-3*k+2,n-k)/(4*n-3*k+2).

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*(k+2)*binomial(4*n-3*k+2, n-k)/(4*n-3*k+2));

Crossrefs

Cf. A002293, A387982.

Sequence in context: A154968 A121582 A239989 * A356459 A226223 A356046

Adjacent sequences: A391375 A391376 A391377 * A391379 A391380 A391381

Keyword

nonn

Author

Seiichi Manyama, Dec 07 2025

Status

approved