A346039 Expansion of e.g.f. Product_{k>=1} exp(1 - exp(x^k))^(1/k!).
1, -1, -1, 3, 1, 17, -119, 165, 1191, -21989, 169527, -317837, -7182779, 54452161, 292654649, -4320853051, -46883217705, 728176373539, 9943868087879, -166076498591597, -2748733072385043, 65290726021558089, 151614363753006601, -11661992771499644571
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..464
Programs
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PARI
my(N=40, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, exp(1-exp(x^k))^(1/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)!))*x^k)))) -
PARI
a(n) = if(n==0, 1, -(n-1)!*sum(k=1, n, k*sumdiv(k, d, 1/(d!*(k/d)!))*a(n-k)/(n-k)!));
Formula
E.g.f.: exp( Sum_{k>=1} (1 - exp(x^k))/k! ).
E.g.f.: exp( -Sum_{k>=1} A121860(k)*x^k/k! ).
a(n) = -(n-1)! * Sum_{k=1..n} k * (Sum_{d|k} 1/(d! * (k/d)!)) * a(n-k)/(n-k)! for n > 0.