OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..444
FORMULA
E.g.f.: exp(Sum_{k>=1} Sum_{j>=1} x^(j*k)/(k*(-j)^(k-1))). - Ilya Gutkovskiy, Sep 12 2018
EXAMPLE
E.g.f.: A(x) = 1 + x + 2*x^2/2! + 12*x^3/3! + 54*x^4/4! + 390*x^5/5! + ...
A(x) = (1+x)*(1 + x^2/2)^2*(1 + x^3/3)^3*(1 + x^4/4)^4*(1 + x^5/5)^5*...
MATHEMATICA
nmax = 20; CoefficientList[Series[Product[(1+x^k/k)^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 07 2020 *)
PROG
(PARI) {a(n)=n!*polcoeff(prod(m=1, n, (1+x^m/m+x*O(x^n))^m), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 02 2010
STATUS
approved