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A365119
G.f. satisfies A(x) = (1 + x / (1 - x*A(x)))^3.
1
1, 3, 6, 19, 69, 267, 1093, 4629, 20142, 89473, 404076, 1849746, 8563558, 40025574, 188612388, 895115942, 4274453904, 20523807009, 99025615998, 479874362583, 2334582421497, 11398055887003, 55828060595832, 274254002718255, 1350907899813921, 6670789629569022
OFFSET
0,2
FORMULA
If g.f. satisfies A(x) = (1 + x/(1 - x*A(x))^s)^t, then a(n) = Sum_{k=0..n} binomial(t*(n-k+1),k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).
PROG
(PARI) a(n, s=1, t=3) = sum(k=0, n, binomial(t*(n-k+1), k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
CROSSREFS
Sequence in context: A058818 A184937 A215817 * A269306 A326317 A306522
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 22 2023
STATUS
approved