A363423 - OEIS

%I #15 Jun 02 2023 10:19:17

%S 1,1,4,40,1126,92440,22559276,16468584194,36033333480881,

%T 236450784546518006,4654297351684653345788,

%U 274836259327539399144691019,48686693681325683653963188907344,25874153864215746591981599665978198380

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

%H Seiichi Manyama, <a href="/A363423/b363423.txt">Table of n, a(n) for n = 0..65</a>

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

%F a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} d * 3^(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, 3*x^k)*x^k/k)+x*O(x^n))); Vec(A);

%Y Cf. A000081, A179470, A363424.

%Y Cf. A359018.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jun 01 2023