OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function
Wikipedia, Lambert W function
FORMULA
a(n) ~ c * n^(n-1), where c = 1/QPochhammer(exp(-1)) = 1.98244090741287370368568246556131... - Vaclav Kotesovec, Jul 21 2018
MATHEMATICA
nmax = 20; CoefficientList[Series[-LambertW[-x]*Product[1/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!
Table[n!*Sum[PartitionsP[n-k]*k^(k-1)/k!, {k, 1, n}], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jul 21 2018
STATUS
approved