cp's OEIS Frontend

A362389 G.f. satisfies A(x) = exp( Sum_{k>=1} (2^k + A(x^k)) * x^k/k ).

%I A362389 #36 Jun 10 2023 10:56:20
%S A362389 1,3,10,34,122,450,1723,6758,27135,110913,460395,1935233,8222504,
%T A362389 35255000,152353021,662892684,2901595559,12768195617,56450822365,
%U A362389 250637657015,1117060889815,4995815027658,22413020866875,100842092305575,454912716037387
%N A362389 G.f. satisfies A(x) = exp( Sum_{k>=1} (2^k + A(x^k)) * x^k/k ).
%H A362389 Seiichi Manyama, <a href="/A362389/b362389.txt">Table of n, a(n) for n = 0..1000</a>
%F A362389 A(x) = B(x)/(1 - 2*x) where B(x) is the g.f. of A363545.
%F A362389 A(x) = Sum_{k>=0} a(k) * x^k = 1/(1-2*x) * 1/Product_{k>=0} (1-x^(k+1))^a(k).
%F A362389 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( 2^k + Sum_{d|k} d * a(d-1) ) * a(n-k).
%o A362389 (PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (2^k+subst(A, x, x^k))*x^k/k)+x*O(x^n))); Vec(A);
%Y A362389 Cf. A001678, A036249, A363541.
%Y A362389 Cf. A029857, A363542, A363545.
%K A362389 nonn
%O A362389 0,2
%A A362389 _Seiichi Manyama_, Jun 09 2023