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A363336
G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^(3*k)) * x^k/k ).
5
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, 82, 94, 111, 128, 144, 170, 196, 222, 257, 297, 335, 388, 447, 506, 580, 668, 754, 863, 990, 1119, 1273, 1460, 1647, 1871, 2138, 2417, 2733, 3118, 3517, 3975, 4522, 5102, 5747, 6529, 7361
OFFSET
0,5
LINKS
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