A371160 Expansion of e.g.f. 1/(1 - x^3 - x^4)^x.

1, 0, 0, 0, 24, 120, 0, 2520, 60480, 544320, 3024000, 59875200, 1277337600, 16086470400, 214313299200, 4903778880000, 104439592857600, 1837718378496000, 38947773376512000, 1008640624223232000, 24160068553420800000, 570728399843137536000

Offset

0,5

Links

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

Formula

a(n) = n! * Sum_{j=0..floor(n/3)} Sum_{k=0..j} binomial(j,n-3*j-k) * |Stirling1(j,k)|/j!.

Prog

(PARI) a(n) = n!*sum(j=0, n\3, sum(k=0, j, binomial(j, n-3*j-k)*abs(stirling(j, k, 1))/j!));

Crossrefs

Cf. A088369, A371159.

Sequence in context: A211594 A211465 A371184 * A371200 A293893 A137799

Adjacent sequences: A371157 A371158 A371159 * A371161 A371162 A371163

Keyword

nonn

Author

Seiichi Manyama, Mar 13 2024

Status

approved