A363336 - OEIS

%I #16 May 31 2023 10:48:57

%S 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 82,94,111,128,144,170,196,222,257,297,335,388,447,506,580,668,754,

%U 863,990,1119,1273,1460,1647,1871,2138,2417,2733,3118,3517,3975,4522,5102,5747,6529,7361

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

%H Seiichi Manyama, <a href="/A363336/b363336.txt">Table of n, a(n) for n = 0..1000</a>

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

%F A(x) * A(w*x) * A(w^2*x) = A(x^3), where w = exp(2*Pi*i/3).

%F 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 (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 Cf. A000081, A115593, A363337.

%Y Cf. A363338.

%K nonn

%O 0,5

%A _Seiichi Manyama_, May 28 2023