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%I #8 Aug 23 2019 18:21:42
%S 1,1,6,32,287,3222,47606,831488,16890792,389286222,10037183606,
%T 286154919078,8937624574652,303483905672078,11130904101218094,
%U 438532313635906858,18470060947222927499,828155619735377936654,39384843256547964375436,1980138439071577626157382
%N G.f.: B(x)*B(2*x^2)*B(3*x^3)*..., where B(x) is g.f. of A000312.
%H Alois P. Heinz, <a href="/A326985/b326985.txt">Table of n, a(n) for n = 0..386</a>
%F a(n) ~ n^n.
%p B:= proc(n) option remember; n^n end:
%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i=1,
%p B(n), add(b(j, 1)*i^j*b(n-i*j, i-1), j=0..n/i)))
%p end:
%p a:= n-> b(n$2):
%p seq(a(n), n=0..20); # _Alois P. Heinz_, Aug 23 2019
%t nmax = 20; CoefficientList[Series[Product[1+Sum[k^k*j^k*x^(j*k), {k, 1, nmax/j}], {j, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A000312, A110143, A326986.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Aug 10 2019
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