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A365111
G.f. satisfies A(x) = 1 + x / (1 + x*A(x))^4.
4
1, 1, -4, 6, 16, -119, 240, 630, -5656, 13044, 31568, -323102, 816172, 1772553, -20373748, 55339784, 105991968, -1366239119, 3950894080, 6570520544, -95534073488, 292319792622, 414994066768, -6884779019086, 22198354364212, 26341578132594, -507524582140912
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=4) = 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