A387546 Coefficient of x^n in the expansion of ( (1-x+x^5) / (1-x) )^n.

1, 0, 0, 0, 0, 5, 6, 7, 8, 9, 55, 121, 210, 325, 469, 1100, 2536, 5185, 9555, 16264, 30895, 63721, 131615, 260360, 487394, 918155, 1793051, 3589470, 7169365, 13984699, 26948686, 52250252, 102705512, 203469673, 401217323, 784970632, 1531810155, 3000289189

Offset

0,6

Links

Table of n, a(n) for n=0..37.

Formula

a(n) = Sum_{k=0..floor(n/5)} binomial(n,k) * binomial(n-4*k-1,n-5*k).

The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-x) / (1-x+x^5) ). See A365702.

Prog

(PARI) a(n, s=5, t=1, u=1) = sum(k=0, n\s, binomial(t*n, k)*binomial((u-t+1)*n-(s-1)*k-1, n-s*k));

Crossrefs

Cf. A088218, A246437, A372413, A387345.

Cf. A365702.

Sequence in context: A250050 A051052 A377265 * A119368 A088721 A325435

Adjacent sequences: A387543 A387544 A387545 * A387547 A387548 A387549

Keyword

nonn

Author

Seiichi Manyama, Sep 29 2025

Status

approved