A323634 Expansion of Product_{k>=1} 1/(1 - k^(k-1)*x^k).
1, 1, 3, 12, 80, 723, 8716, 128227, 2251086, 45647542, 1051845574, 27107414480, 772785074811, 24136982014698, 819697939365724, 30068912837398063, 1184872370227462528, 49914074776385885492, 2238476211786621770206, 106476394492364281869654, 5354276181476337307494676
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..387
Programs
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Maple
a:=series(mul(1/(1-k^(k-1)*x^k),k=1..100),x=0,21): seq(coeff(a,x,n),n=0..20); # Paolo P. Lava, Apr 02 2019
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Mathematica
nmax = 20; CoefficientList[Series[Product[1/(1 - k^(k - 1) x^k), {k, 1, nmax}], {x, 0, nmax}], x] a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d^(k - k/d + 1), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 20}] -
PARI
N=40; x='x+O('x^N); Vec(1/prod(k=1, N, 1-k^(k-1)*x^k)) \\ Seiichi Manyama, Aug 22 2020
Formula
a(n) ~ n^(n-1) * (1 + exp(-1)/n + (3*exp(-2) + 3*exp(-1)/2)/n^2). - Vaclav Kotesovec, Jan 22 2019
Comments