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A309652 a(n) = [x^n] B(x)^n, where B(x) is g.f. of A000312.

%I A309652 #10 Aug 24 2019 15:09:36
%S A309652 1,1,9,106,1493,24276,448122,9301251,215547845,5541171496,
%T A309652 156997349684,4870353700532,164366482285898,5998207807965543,
%U A309652 235388194276592723,9884482616014596546,442206843338189113445,20995082225203329126384,1054247070579064423466016
%N A309652 a(n) = [x^n] B(x)^n, where B(x) is g.f. of A000312.
%H A309652 Alois P. Heinz, <a href="/A309652/b309652.txt">Table of n, a(n) for n = 0..385</a>
%F A309652 a(n) ~ exp(exp(-1)) * n^(n+1).
%p A309652 B:= proc(n) option remember; n^n end:
%p A309652 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i=1, B(n),
%p A309652       (h-> add(b(j, h)*b(n-j, i-h), j=0..n))(iquo(i, 2))))
%p A309652     end:
%p A309652 a:= n-> b(n$2):
%p A309652 seq(a(n), n=0..20);  # _Alois P. Heinz_, Aug 23 2019
%t A309652 Table[SeriesCoefficient[(1+Sum[k^k*x^k, {k, 1, n}])^n, {x, 0, n}], {n, 0, 20}]
%Y A309652 Cf. A287899, A326985, A326986.
%K A309652 nonn
%O A309652 0,3
%A A309652 _Vaclav Kotesovec_, Aug 11 2019