cp's OEIS Frontend

A363336 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^(3*k)) * x^k/k ).

%I A363336 #16 May 31 2023 10:48:57
%S A363336 1,1,1,1,2,2,2,3,4,4,5,6,7,9,11,12,15,18,20,23,29,33,38,45,52,60,72,
%T A363336 82,94,111,128,144,170,196,222,257,297,335,388,447,506,580,668,754,
%U A363336 863,990,1119,1273,1460,1647,1871,2138,2417,2733,3118,3517,3975,4522,5102,5747,6529,7361
%N A363336 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^(3*k)) * x^k/k ).
%H A363336 Seiichi Manyama, <a href="/A363336/b363336.txt">Table of n, a(n) for n = 0..1000</a>
%F A363336 A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{k>=0} (1-x^(3*k+1))^a(k).
%F A363336 A(x) * A(w*x) * A(w^2*x) = A(x^3), where w = exp(2*Pi*i/3).
%F A363336 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k and d==1 mod 3} d * a(floor(d/3)) ) * a(n-k).
%o A363336 (PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, subst(A, x, x^(3*k))*x^k/k)+x*O(x^n))); Vec(A);
%Y A363336 Cf. A000081, A115593, A363337.
%Y A363336 Cf. A363338.
%K A363336 nonn
%O A363336 0,5
%A A363336 _Seiichi Manyama_, May 28 2023