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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 07 2018
STATUS
approved