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A302399
Expansion of e.g.f. Product_{k>=1} 1/(1 - exp(x)*x^k)^k.
1
1, 1, 8, 63, 628, 7405, 103266, 1630195, 28812344, 561715353, 11971270270, 276322667071, 6867229990644, 182651988444133, 5174629835814362, 155498722020145995, 4938797154614179696, 165259917542803746097, 5809661798192528407542, 214032701720169039806551, 8244827039453943163648940
OFFSET
0,3
FORMULA
E.g.f.: Product_{k>=1} 1/(1 - exp(x)*x^k)^k.
a(n) ~ c * n! / LambertW(1)^n, where c = 1/(1 + LambertW(1)) * Product_{j>=1} 1/(1 - LambertW(1)^j)^(j+1) = 115.50749040505570853455997830821388214033876679679... - Vaclav Kotesovec, Apr 07 2018
EXAMPLE
Product_{k>=1} 1/(1 - exp(x)*x^k)^k = 1 + x/1! + 8*x^2/2! + 63*x^3/3! + 628*x^4/4! + 7405*x^5/5! + 103266*x^6/6! + ...
MAPLE
a:=series(mul(1/(1-exp(x)*x^k)^k, k=1..100), x=0, 21): seq(n!*coeff(a, x, n), n=0..20); # Paolo P. Lava, Mar 26 2019
MATHEMATICA
nmax = 20; CoefficientList[Series[Product[1/(1 - Exp[x] x^k)^k, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
CROSSREFS
Sequence in context: A105219 A060071 A037205 * A356337 A084096 A361238
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 07 2018
STATUS
approved