A365798 G.f. satisfies A(x) = 1 + x*A(x)*(1 + x^5*A(x)^4).

1, 1, 1, 1, 1, 1, 2, 7, 22, 57, 127, 253, 468, 848, 1618, 3433, 8009, 19384, 46264, 106369, 235179, 505955, 1079790, 2332555, 5166405, 11737860, 27086236, 62676956, 144074416, 327837356, 739787486, 1663922487, 3751649542, 8513640107, 19464624667

Offset

0,7

Links

Table of n, a(n) for n=0..34.

Formula

a(n) = Sum_{k=0..floor(n/6)} binomial(n-5*k,k) * binomial(n-k+1,n-5*k) / (n-k+1) = Sum_{k=0..floor(n/6)} binomial(n-k,5*k) * binomial(5*k,k) / (4*k+1).

Prog

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

Crossrefs

Cf. A063019, A182454, A349311, A364539, A364522.

Cf. A005708, A364523, A365732, A365733.

Cf. A002294, A365736.

Sequence in context: A323228 A348290 A099132 * A139398 A365736 A364522

Adjacent sequences: A365795 A365796 A365797 * A365799 A365800 A365801

Keyword

nonn

Author

Seiichi Manyama, Sep 19 2023

Status

approved