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A363439
G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * (3*x)^k/k ).
3
1, 3, 18, 108, 702, 4698, 32913, 236844, 1747170, 13131639, 100239444, 774932832, 6055105590, 47742847875, 379381851684, 3035174325246, 24426965179593, 197622494260479, 1606332527049645, 13111628672610153, 107428845309125157
OFFSET
0,2
LINKS
FORMULA
A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{k>=0} (1-3*x^(k+1))^a(k).
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} d * 3^(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, subst(A, x, x^k)*(3*x)^k/k)+x*O(x^n))); Vec(A);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 02 2023
STATUS
approved