OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..445
FORMULA
E.g.f.: exp(Sum_{k>=1} Sum_{j>=1} (1 + (-1)^(k+1))*x^(j*k)/(k*j^k)).
a(n) ~ sqrt(Pi/2) * n^(n + 5/2) / exp(n + 2*gamma), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Mar 26 2019
MAPLE
a:=series(mul((1+x^k/k)/(1-x^k/k), k=1..100), x=0, 22): seq(n!*coeff(a, x, n), n=0..21); # Paolo P. Lava, Mar 26 2019
MATHEMATICA
nmax = 21; CoefficientList[Series[Product[(1 + x^k/k)/(1 - x^k/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 21; CoefficientList[Series[Exp[Sum[Sum[(1 + (-1)^(k + 1)) x^(j k)/(k j^k), {j, 1, nmax}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 27 2018
STATUS
approved