A365730 G.f. satisfies A(x) = 1 + x^4*A(x)^4*(1 + x*A(x)).

1, 0, 0, 0, 1, 1, 0, 0, 4, 9, 5, 0, 22, 78, 91, 35, 140, 680, 1224, 969, 1254, 5985, 14630, 17710, 17710, 55660, 164450, 269100, 299520, 593775, 1805076, 3681405, 4951692, 7594752, 20173560, 47303520, 76404460, 110676324, 239784864, 589602585, 1106339923

Offset

0,9

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A365727, A365728, A365729, A365731.

Cf. A001005, A001006, A365724.

Cf. A215341.

Sequence in context: A087369 A200629 A021206 * A121305 A002904 A200396

Adjacent sequences: A365727 A365728 A365729 * A365731 A365732 A365733

Keyword

nonn

Author

Seiichi Manyama, Sep 17 2023

Status

approved