A365723 G.f. satisfies A(x) = 1 + x^3*A(x)^2*(1 + x*A(x)).

1, 0, 0, 1, 1, 0, 2, 5, 3, 5, 21, 28, 26, 84, 180, 207, 385, 990, 1562, 2288, 5278, 10439, 15925, 30212, 64738, 112268, 192780, 396338, 761634, 1317840, 2512940, 5015867, 9146049, 16729462, 32927950, 62851525, 115101637, 220051350, 427898900, 800956600, 1505524800

Offset

0,7

Links

Table of n, a(n) for n=0..40.

Formula

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

Prog

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

Crossrefs

Cf. A308616, A365724, A365725, A365726.

Cf. A365694.

Sequence in context: A248852 A299210 A104978 * A124568 A091807 A085825

Adjacent sequences: A365720 A365721 A365722 * A365724 A365725 A365726

Keyword

nonn

Author

Seiichi Manyama, Sep 17 2023

Status

approved