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A365109
G.f. satisfies A(x) = 1 + x / (1 + x*A(x))^2.
3
1, 1, -2, 1, 6, -18, 8, 89, -266, 62, 1684, -4710, -220, 35648, -91236, -34871, 803302, -1856874, -1448844, 18809694, -38816620, -48910700, 451491680, -820626294, -1522994404, 11015923292, -17319046712, -45512957516, 271664145264, -359911736252, -1327355044924
OFFSET
0,3
FORMULA
If g.f. satisfies A(x) = 1 + x/(1 + x*A(x))^s, then a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-k+1,k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).
PROG
(PARI) a(n, s=2) = sum(k=0, n, (-1)^(n-k)*binomial(n-k+1, k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Aug 22 2023
STATUS
approved