A371273 E.g.f. satisfies A(x) = 1 + x*A(x)^4 * (exp(x*A(x)^3) - 1).

1, 0, 2, 3, 172, 1025, 54606, 710017, 38964024, 855167553, 49992166090, 1603665906161, 101454726848388, 4342187407054081, 299554876119595110, 16084216120063348545, 1213404824364026124016, 78279943651487041769345, 6456915976418046368634402

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = (n!/(3*n+1)!) * Sum_{k=0..floor(n/2)} (3*n+k)! * Stirling2(n-k,k)/(n-k)!.

Prog

(PARI) a(n) = n!*sum(k=0, n\2, (3*n+k)!*stirling(n-k, k, 2)/(n-k)!)/(3*n+1)!;

Crossrefs

Cf. A370988, A371271.

Cf. A371232.

Sequence in context: A115231 A371231 A042369 * A328257 A042701 A371232

Adjacent sequences: A371270 A371271 A371272 * A371274 A371275 A371276

Keyword

nonn

Author

Seiichi Manyama, Mar 16 2024

Status

approved