A345751 E.g.f.: Product_{k>=1} (1 - (exp(x) - 1)^k)^(1/k).

1, -1, -2, -3, -3, 40, 477, 4375, 45154, 486817, 5002397, 54970652, 732601449, 10046371231, 113632306694, 1051655108629, 12585372336141, 202763995934160, -863641466773595, -247388278229558697, -10810815349601723990, -311011007642247422759

Offset

0,3

Comments

Stirling transform of A028343.

Links

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

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Stirling Transform

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) * A028343(k).

Mathematica

max = 21; Range[0, max]! * CoefficientList[Series[Product[(1 - (Exp[x] - 1)^k)^(1/k), {k, 1, max}], {x, 0, max}], x] (* Amiram Eldar, Jun 26 2021 *)

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1-(exp(x)-1)^k)^(1/k))))
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(-sum(k=1, N, numdiv(k)*(exp(x)-1)^k/k))))

Crossrefs

Cf. A000005, A028343, A048993, A336100, A345750, A345751, A345752.

Sequence in context: A100650 A096502 A101462 * A242786 A214219 A365223

Adjacent sequences: A345748 A345749 A345750 * A345752 A345753 A345754

Keyword

sign

Author

Seiichi Manyama, Jun 26 2021

Status

approved