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A364399
G.f. satisfies A(x) = 1 + x/A(x)^3*(1 + 1/A(x)^2).
6
1, 2, -16, 212, -3400, 60384, -1142960, 22598832, -461250208, 9644611008, -205537131008, 4447969973888, -97482797466624, 2159242220999936, -48260706692535552, 1087076798266594048, -24652590023639251456, 562396337623786449920
OFFSET
0,2
FORMULA
G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A363380.
a(n) = (-1)^(n-1) * (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(4*n+2*k-2,n-1) for n > 0.
a(n) ~ c*(-1)^(n-1)*256^n*27^(-n)*3F2([-n, 2*n, 2*n-1/2], [3*n/2, (3*n+1)/2], -1)*n^(-3/2), with c = (1/8)*sqrt(3/(2*Pi)). - Stefano Spezia, Oct 21 2023
PROG
(PARI) a(n) = if(n==0, 1, (-1)^(n-1)*sum(k=0, n, binomial(n, k)*binomial(4*n+2*k-2, n-1))/n);
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jul 22 2023
STATUS
approved