A345749 E.g.f.: Product_{k>=1} 1/(1 - (exp(x) - 1)^k)^(1/k).

1, 1, 4, 21, 147, 1250, 12633, 147497, 1947676, 28699373, 466994003, 8309274754, 160368858609, 3336869582657, 74468098634660, 1773827462044421, 44905503103938915, 1203843692164105458, 34070243272290551113, 1015056385225183643721

Offset: 0

Author

Seiichi Manyama, Jun 26 2021

Keywords

• nonn

Comments

Stirling transform of A028342.

Links

• N. J. A. Sloane, Transforms
• Eric Weisstein's World of Mathematics, Stirling Transform

Crossrefs

Cf. A000005, A028342, A048993, A167137, A294363, A305986, A345750, A345751.

Programs

Mathematica

max = 19; Range[0, max]! * CoefficientList[Series[Product[1/(1 - (Exp[x] - 1)^k)^(1/k), {k, 1, max}], {x, 0, max}], x] (* Amiram Eldar, Jun 26 2021 *)

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-(exp(x)-1)^k)^(1/k))))

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N,numdiv(k)*(exp(x)-1)^k/k))))

Formula

E.g.f.: exp( Sum_{k>=1} d(k) * (exp(x) - 1)^k / k ), where d(n) is the number of divisors of n.

a(n) = Sum_{k=0..n} Stirling2(n,k) * A028342(k).