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
Keywords
Links
- N. J. A. Sloane, Transforms
- Eric Weisstein's World of Mathematics, Stirling Transform
Programs
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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 *) -
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))))
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).
Comments