A373685 Expansion of e.g.f. exp(x / (1 - x^3)^2) / (1 - x^3).

1, 1, 1, 7, 73, 301, 1561, 32131, 306097, 2062873, 43102801, 720515071, 7245589561, 136364378437, 3259345980073, 47903339552251, 873735377165281, 25383884535029041, 515592396859327777, 10003196649764818423, 316630570292623967401, 8359224513085985870941

Offset

0,4

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} binomial(2*n-5*k,k)/(n-3*k)!.

a(n) == 1 (mod 6).

Prog

(PARI) a(n) = n!*sum(k=0, n\3, binomial(2*n-5*k, k)/(n-3*k)!);

Crossrefs

Cf. A373680, A373684.

Sequence in context: A012158 A139966 A175205 * A027017 A076106 A202042

Adjacent sequences: A373682 A373683 A373684 * A373686 A373687 A373688

Keyword

nonn

Author

Seiichi Manyama, Jun 13 2024

Status

approved