OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..537
FORMULA
E.g.f.: exp( Sum_{k>=1} (1 - exp(x^k/k!)) ).
E.g.f.: exp( -Sum_{k>=1} A038041(k)*x^k/k! ).
a(n) = -(n-1)! * Sum_{k=1..n} k * (Sum_{d|k} 1/(d! * (k/d)!^d)) * a(n-k)/(n-k)! for n > 0.
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, exp(1-exp(x^k/k!)))))
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, 1-exp(x^k/k!)))))
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(-sum(k=1, N, sumdiv(k, d, 1/(d!*(k/d)!^d))*x^k))))
(PARI) a(n) = if(n==0, 1, -(n-1)!*sum(k=1, n, k*sumdiv(k, d, 1/(d!*(k/d)!^d))*a(n-k)/(n-k)!));
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jul 02 2021
STATUS
approved