A363541 - OEIS

A363541

G.f. satisfies A(x) = exp( Sum_{k>=1} (3^k + A(x^k)) * x^k/k ).

%I #19 Jun 10 2023 10:56:16

%S 1,4,17,73,324,1469,6838,32490,157398,775010,3870690,19567202,

%T 99957231,515250057,2676884745,14002926871,73693381322,389904743248,

%U 2072794614996,11066421965311,59310040841395,318978744562253,1720962766007827

%N G.f. satisfies A(x) = exp( Sum_{k>=1} (3^k + A(x^k)) * x^k/k ).

%H Seiichi Manyama, <a href="/A363541/b363541.txt">Table of n, a(n) for n = 0..1000</a>

%F A(x) = B(x)/(1 - 3*x) where B(x) is the g.f. of A363546.

%F A(x) = Sum_{k>=0} a(k) * x^k = 1/(1-3*x) * 1/Product_{k>=0} (1-x^(k+1))^a(k).

%F a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( 3^k + Sum_{d|k} d * a(d-1) ) * a(n-k).

%o (PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (3^k+subst(A, x, x^k))*x^k/k)+x*O(x^n))); Vec(A);

%Y Cf. A001678, A036249, A362389.

%Y Cf. A363507, A363543, A363546.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jun 09 2023