OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..410
FORMULA
a(0) = 1 and a(n) = (n-1)! * Sum_{k=1..n} k^2*A000041(k)*a(n-k)/(n-k)! for n > 0.
EXAMPLE
a(5) = 4! * (1^2*1*a(4)/4! + 2^2*2*a(3)/3! + 3^2*3*a(2)/2! + 4^2*5*a(1)/1! + 5^2*7*a(0)/0!) = 12501.
MATHEMATICA
nmax = 20; CoefficientList[Series[E^Sum[k*PartitionsP[k]*x^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 18 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 15 2017
STATUS
approved