A363424 - OEIS

%I #14 Jun 02 2023 10:19:14

%S 1,1,5,85,5535,1422815,1458410395,5975113492155,97902240525033630,

%T 6416219161308006188750,1681979772433159156954845846,

%U 1763685303864317080584539713676102,7397434088431352859937186709876628421294

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

%H Seiichi Manyama, <a href="/A363424/b363424.txt">Table of n, a(n) for n = 0..58</a>

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

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

%Y Cf. A000081, A179470, A363423.

%Y Cf. A359186.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jun 01 2023