A365727 G.f. satisfies A(x) = 1 + x^4*A(x)*(1 + x*A(x)).

1, 0, 0, 0, 1, 1, 0, 0, 1, 3, 2, 0, 1, 6, 10, 5, 1, 10, 30, 35, 15, 15, 70, 140, 127, 63, 140, 420, 631, 490, 384, 1050, 2311, 2808, 2136, 2739, 6931, 12057, 12672, 11055, 19449, 42097, 61050, 60060, 66353, 131054, 241670, 306735, 308881, 428792, 835614, 1337765

Offset

0,10

Links

Table of n, a(n) for n=0..51.

Formula

a(n) = Sum_{k=0..floor(n/4)} binomial(k,n-4*k) * binomial(n-3*k+1,k) / (n-3*k+1).

Prog

(PARI) a(n) = sum(k=0, n\4, binomial(k, n-4*k)*binomial(n-3*k+1, k)/(n-3*k+1));

Crossrefs

Cf. A365728, A365729, A365730, A365731.

Cf. A023427.

Sequence in context: A081576 A330785 A292717 * A054654 A355423 A345066

Adjacent sequences: A365724 A365725 A365726 * A365728 A365729 A365730

Keyword

nonn

Author

Seiichi Manyama, Sep 17 2023

Status

approved