OFFSET
0,5
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{k>=0} (1-x^(3*k+1))^a(k).
A(x) * A(w*x) * A(w^2*x) = A(x^3), where w = exp(2*Pi*i/3).
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).
PROG
(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);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 28 2023
STATUS
approved