A365729 G.f. satisfies A(x) = 1 + x^4*A(x)^3*(1 + x*A(x)).

1, 0, 0, 0, 1, 1, 0, 0, 3, 7, 4, 0, 12, 45, 55, 22, 55, 286, 546, 455, 413, 1820, 4760, 6120, 5304, 12597, 38760, 67830, 73587, 108262, 309925, 672980, 928763, 1171390, 2598310, 6270030, 10607025, 14033565, 24293880, 57256875, 112293597, 167416275, 255805056

Offset

0,9

Links

Table of n, a(n) for n=0..42.

Formula

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

Prog

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

Crossrefs

Cf. A365727, A365728, A365730, A365731.

Cf. A365697.

Sequence in context: A050393 A110778 A200129 * A181912 A108297 A135928

Adjacent sequences: A365726 A365727 A365728 * A365730 A365731 A365732

Keyword

nonn

Author

Seiichi Manyama, Sep 17 2023

Status

approved