A355100 E.g.f. A(x) satisfies A(x) = 1 + 2 * x * A(exp(x) - 1).

1, 2, 8, 60, 688, 11060, 234744, 6314196, 208825376, 8296326612, 388694773720, 21155834296476, 1321107368127408, 93662776272057356, 7471576015922028248, 665418775120254506940, 65714704859545872003008, 7153378915302503698953860

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(0) = 1; a(n) = 2 * n * Sum_{k=0..n-1} Stirling2(n-1,k) * a(k).

a(n) = 2 * n * A355083(n-1) for n>0.

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=2*i*sum(j=0, i-1, stirling(i-1, j, 2)*v[j+1])); v;

Crossrefs

Cf. A048801, A355101.

Cf. A355083.

Sequence in context: A303672 A303062 A001188 * A303532 A355106 A113145

Adjacent sequences: A355097 A355098 A355099 * A355101 A355102 A355103

Keyword

nonn

Author

Seiichi Manyama, Jun 19 2022

Status

approved