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G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * (4 + A(x^k)) * x^k/k ).
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%I #14 Jun 07 2023 09:45:05

%S 1,5,15,50,190,766,3231,14066,62681,284591,1311622,6120183,28855529,

%T 137257541,657894518,3174411715,15406640415,75162477018,368383443235,

%U 1813007892858,8956214966017,44393932344984,220732441125743,1100621484436502

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

%H Seiichi Manyama, <a href="/A363510/b363510.txt">Table of n, a(n) for n = 0..1000</a>

%F A(x) = Sum_{k>=0} a(k) * x^k = (1+x)^4 * Product_{k>=0} (1+x^(k+1))^a(k).

%F 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 (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 Cf. A004111, A038075, A038076, A363509.

%Y Cf. A363508.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jun 06 2023