A394853 Expansion of g^7/(6-5*g)^4, where g = 1+x*g^6 is the g.f. of A002295.

1, 27, 573, 11014, 200430, 3522192, 60410931, 1017759852, 16912317690, 277987524585, 4528956441933, 73245184338192, 1177252129217840, 18821776752970380, 299546153329805190, 4748217853797986904, 75001137437207696130, 1180992084793962172290

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

G.f.: (Sum_{k>=0} binomial(6*k+3,k) * x^k) * (Sum_{k>=0} binomial(6*k,k) * x^k)^3.

Sum_{k>=1} a(k-1) * x^k/k^2 = (1/12) * log( Sum_{k>=0} binomial(6*k+6,k) * x^k ).

a(n) = ((n+1)/12) * (binomial(6*n+5,n) + Sum_{k=0..n+1} 5^(n+1-k) * binomial(6*n+6,k)).

a(n) = ((n+1)/10) * Sum_{k=0..n+1} 5^(n+1-k) * binomial(6*n+5,k).

a(n) = Sum_{k=0..n} 5^k * binomial(k+2,2) * binomial(6*n+6,n-k).

Prog

(PARI) a(n) = (n+1)*(binomial(6*n+5, n)+sum(k=0, n+1, 5^(n+1-k)*binomial(6*n+6, k)))/12;

Crossrefs

Cf. A378504, A395664, A395665, A395667, A395675.

Cf. A002295, A004356.

Sequence in context: A267544 A061914 A076008 * A232944 A185891 A185883

Adjacent sequences: A394850 A394851 A394852 * A394854 A394855 A394856

Keyword

nonn

Author

Seiichi Manyama, May 03 2026

Status

approved