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A363508 G.f. satisfies A(x) = exp( Sum_{k>=1} (4 + A(x^k)) * x^k/k ).

%I A363508 #14 Jun 07 2023 00:08:14
%S A363508 1,5,20,80,340,1516,7046,33736,165436,826566,4193348,21542664,
%T A363508 111848161,585949358,3093526496,16442687695,87914559018,472522551440,
%U A363508 2551591234444,13836226412386,75311992329508,411336641019998,2253641429297336
%N A363508 G.f. satisfies A(x) = exp( Sum_{k>=1} (4 + A(x^k)) * x^k/k ).
%H A363508 Seiichi Manyama, <a href="/A363508/b363508.txt">Table of n, a(n) for n = 0..1000</a>
%F A363508 A(x) = Sum_{k>=0} a(k) * x^k = 1/(1-x)^4 * 1/Product_{k>=0} (1-x^(k+1))^a(k).
%F A363508 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( 4 + Sum_{d|k} d * a(d-1) ) * a(n-k).
%o A363508 (PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (4+subst(A, x, x^k))*x^k/k)+x*O(x^n))); Vec(A);
%Y A363508 Cf. A000081, A029857, A036249, A363507.
%Y A363508 Cf. A363510.
%K A363508 nonn
%O A363508 0,2
%A A363508 _Seiichi Manyama_, Jun 06 2023