A373684 Expansion of e.g.f. exp(x / (1 - x^3)) / (1 - x^3).

1, 1, 1, 7, 49, 181, 1201, 16171, 122977, 971209, 16788961, 206578351, 2094314641, 40260673597, 694617709969, 9088535091091, 187060085419201, 4109646055718161, 68029103349383617, 1498126927153125079, 39199612737165358321, 799248202624341298501

Offset

0,4

Links

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

Formula

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

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

Prog

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

Crossrefs

Cf. A002720, A373683.

Cf. A293493.

Sequence in context: A163827 A206989 A221962 * A294292 A015953 A206931

Adjacent sequences: A373681 A373682 A373683 * A373685 A373686 A373687

Keyword

nonn

Author

Seiichi Manyama, Jun 13 2024

Status

approved