A395656 Expansion of 1/(9*x) * (1/(4-3*g)^3 - 1), where g = 1+x*g^4 is the g.f. of A002293.

1, 10, 100, 995, 9852, 97144, 954540, 9351945, 91397260, 891337624, 8676673168, 84327075545, 818401761220, 7932693938760, 76804617216840, 742874557254885, 7178721120223020, 69313564579177240, 668744574950480560, 6447636717495742540, 62124533086188443760

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = A395659(n)/(n+1) = (1/(n+1)) * Sum_{k=0..n} 3^k * binomial(k+3,3) * binomial(4*n+4,n-k).

Prog

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

Crossrefs

Cf. A001700, A395655, A395657.

Cf. A002293, A395659.

Sequence in context: A272501 A171284 A125897 * A182979 A355892 A396192

Adjacent sequences: A395653 A395654 A395655 * A395657 A395658 A395659

Keyword

nonn

Author

Seiichi Manyama, May 02 2026

Status

approved