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A363510
G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * (4 + A(x^k)) * x^k/k ).
3
1, 5, 15, 50, 190, 766, 3231, 14066, 62681, 284591, 1311622, 6120183, 28855529, 137257541, 657894518, 3174411715, 15406640415, 75162477018, 368383443235, 1813007892858, 8956214966017, 44393932344984, 220732441125743, 1100621484436502
OFFSET
0,2
LINKS
FORMULA
A(x) = Sum_{k>=0} a(k) * x^k = (1+x)^4 * Product_{k>=0} (1+x^(k+1))^a(k).
a(0) = 1; a(n) = (-1/n) * Sum_{k=1..n} ( 4 * (-1)^k + Sum_{d|k} (-1)^(k/d) * d * a(d-1) ) * a(n-k).
PROG
(PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (-1)^(k+1)*(4+subst(A, x, x^k))*x^k/k)+x*O(x^n))); Vec(A);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 06 2023
STATUS
approved