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A363510 G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * (4 + A(x^k)) * x^k/k ).

%I A363510 #14 Jun 07 2023 09:45:05
%S A363510 1,5,15,50,190,766,3231,14066,62681,284591,1311622,6120183,28855529,
%T A363510 137257541,657894518,3174411715,15406640415,75162477018,368383443235,
%U A363510 1813007892858,8956214966017,44393932344984,220732441125743,1100621484436502
%N A363510 G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * (4 + A(x^k)) * x^k/k ).
%H A363510 Seiichi Manyama, <a href="/A363510/b363510.txt">Table of n, a(n) for n = 0..1000</a>
%F A363510 A(x) = Sum_{k>=0} a(k) * x^k = (1+x)^4 * Product_{k>=0} (1+x^(k+1))^a(k).
%F A363510 a(0) = 1; a(n) = (-1/n) * Sum_{k=1..n} ( 4 * (-1)^k + Sum_{d|k} (-1)^(k/d) * d * a(d-1) ) * a(n-k).
%o A363510 (PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (-1)^(k+1)*(4+subst(A, x, x^k))*x^k/k)+x*O(x^n))); Vec(A);
%Y A363510 Cf. A004111, A038075, A038076, A363509.
%Y A363510 Cf. A363508.
%K A363510 nonn
%O A363510 0,2
%A A363510 _Seiichi Manyama_, Jun 06 2023