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A363541
G.f. satisfies A(x) = exp( Sum_{k>=1} (3^k + A(x^k)) * x^k/k ).
6
1, 4, 17, 73, 324, 1469, 6838, 32490, 157398, 775010, 3870690, 19567202, 99957231, 515250057, 2676884745, 14002926871, 73693381322, 389904743248, 2072794614996, 11066421965311, 59310040841395, 318978744562253, 1720962766007827
OFFSET
0,2
LINKS
FORMULA
A(x) = B(x)/(1 - 3*x) where B(x) is the g.f. of A363546.
A(x) = Sum_{k>=0} a(k) * x^k = 1/(1-3*x) * 1/Product_{k>=0} (1-x^(k+1))^a(k).
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( 3^k + Sum_{d|k} d * a(d-1) ) * a(n-k).
PROG
(PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (3^k+subst(A, x, x^k))*x^k/k)+x*O(x^n))); Vec(A);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 09 2023
STATUS
approved