A370674 Expansion of Sum_{k>0} k! * x^k/(1+x^k)^(k+1).
1, 0, 9, 14, 125, 702, 5047, 40172, 362949, 3628100, 39916811, 478996746, 6227020813, 87178250922, 1307674370745, 20922789524192, 355687428096017, 6402373702119096, 121645100408832019, 2432902008136718030, 51090942171709621965, 1124000727777128678510
Offset: 1
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k!*x^k/(1+x^k)^(k+1))) -
PARI
a(n) = sumdiv(n, d, (-1)^(d-1)*(d+n/d-1)!/(d-1)!);
Formula
a(n) = Sum_{d|n} (-1)^(d-1) * (d+n/d-1)!/(d-1)!.
If p is an odd prime, a(p) = p + p!.