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A326986 G.f.: B(x)*B(x^2)*B(x^3)*..., where B(x) is g.f. of A000312.

%I A326986 #9 Aug 23 2019 18:20:42
%S A326986 1,1,5,29,266,3163,46994,827107,16828741,388308078,10017853262,
%T A326986 285720195351,8926575094978,303172417424680,11121259586618456,
%U A326986 438207141286916539,18458204444260001120,827690809585441201775,39365349178064541861252,1979267564496263599093676
%N A326986 G.f.: B(x)*B(x^2)*B(x^3)*..., where B(x) is g.f. of A000312.
%H A326986 Alois P. Heinz, <a href="/A326986/b326986.txt">Table of n, a(n) for n = 0..386</a>
%F A326986 a(n) ~ n^n.
%p A326986 B:= proc(n) option remember; n^n end:
%p A326986 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i=1,
%p A326986       B(n), add(b(j, 1)*b(n-i*j, i-1), j=0..n/i)))
%p A326986     end:
%p A326986 a:= n-> b(n$2):
%p A326986 seq(a(n), n=0..20);  # _Alois P. Heinz_, Aug 23 2019
%t A326986 nmax = 20; CoefficientList[Series[Product[1+Sum[k^k*x^(j*k), {k, 1, nmax/j}], {j, 1, nmax}], {x, 0, nmax}], x]
%Y A326986 Cf. A000312, A096161, A309652, A326985.
%K A326986 nonn
%O A326986 0,3
%A A326986 _Vaclav Kotesovec_, Aug 10 2019