A395800 Expansion of -1/(Sum_{k>=0} binomial(5*k+3,k) * x^k).

-1, 8, 14, 80, 595, 5016, 45540, 434304, 4289780, 43501640, 450266674, 4737547360, 50520394470, 544805327400, 5931061593120, 65096002327296, 719512200316140, 8002078308422440, 89481679308557550, 1005472614647991600, 11347246369917801369, 128560385140949059760

Offset

0,2

Links

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

Formula

G.f.: -1/B(x) where B(x) is the g.f. of A394565.

G.f.: (4*g-5)/g^4 where g = 1+x*g^5 is the g.f. of A002294.

a(n) = (1/n) * (8*binomial(5*n-5,n-1) - 12*binomial(5*n-5,n-2)) for n > 0.

a(n) = (1/n) * (20*binomial(5*n-5,n-1) - 12*binomial(5*n-4,n-1)) for n > 0.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(-1/sum(k=0, N, binomial(5*k+3, k)*x^k))

Crossrefs

Cf. A124724, A337292, A395798, A395799.

Cf. A002294, A394565.

Sequence in context: A236553 A050582 A128451 * A177170 A275006 A219778

Adjacent sequences: A395797 A395798 A395799 * A395801 A395802 A395803

Keyword

sign,easy

Author

Seiichi Manyama, May 06 2026

Status

approved