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%I #17 Aug 22 2020 11:08:32
%S 1,1,3,12,80,723,8716,128227,2251086,45647542,1051845574,27107414480,
%T 772785074811,24136982014698,819697939365724,30068912837398063,
%U 1184872370227462528,49914074776385885492,2238476211786621770206,106476394492364281869654,5354276181476337307494676
%N Expansion of Product_{k>=1} 1/(1 - k^(k-1)*x^k).
%C This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 1, g(n) = n^(n-1). - _Seiichi Manyama_, Aug 22 2020
%H Seiichi Manyama, <a href="/A323634/b323634.txt">Table of n, a(n) for n = 0..387</a>
%F a(n) ~ n^(n-1) * (1 + exp(-1)/n + (3*exp(-2) + 3*exp(-1)/2)/n^2). - _Vaclav Kotesovec_, Jan 22 2019
%p 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
%t nmax = 20; CoefficientList[Series[Product[1/(1 - k^(k - 1) x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%t 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}]
%o (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
%Y Cf. A023879, A023882, A266964, A299786, A300579.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jan 21 2019
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