A363440 - OEIS

%I #12 Jun 03 2023 09:01:48

%S 1,4,32,256,2208,19712,183808,1763328,17332992,173621248,1766188288,

%T 18196260864,189474570240,1990887063552,21082432966656,

%U 224766598100992,2410570956881920,25988893875994624,281505478557407232,3062014088362049536

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

%H Seiichi Manyama, <a href="/A363440/b363440.txt">Table of n, a(n) for n = 0..938</a>

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

%F a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} d * 4^(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, subst(A, x, x^k)*(4*x)^k/k)+x*O(x^n))); Vec(A);

%Y Cf. A000081, A179469, A363439.

%Y Cf. A363424.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jun 02 2023