A365724 G.f. satisfies A(x) = 1 + x^3*A(x)^3*(1 + x*A(x)).

1, 0, 0, 1, 1, 0, 3, 7, 4, 12, 45, 55, 77, 286, 546, 728, 1960, 4760, 7548, 15504, 39729, 75582, 140448, 336490, 723327, 1366200, 2992990, 6758895, 13522275, 28094040, 63183315, 133231800, 273896532, 600805296, 1305229332, 2720740792, 5843241088, 12797739672

Offset

0,7

Links

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

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(k,n-3*k) * binomial(n+1,k).

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(k, n-3*k)*binomial(n+1, k))/(n+1);

Crossrefs

Cf. A308616, A365723, A365725, A365726.

Cf. A001005, A001006, A365730.

Cf. A114997.

Sequence in context: A352709 A216627 A355927 * A112305 A231396 A231463

Adjacent sequences: A365721 A365722 A365723 * A365725 A365726 A365727

Keyword

nonn

Author

Seiichi Manyama, Sep 17 2023

Status

approved