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A366356
G.f. satisfies A(x) = 1/(1 - x) + x/A(x).
6
1, 2, -1, 6, -17, 71, -292, 1284, -5807, 26961, -127627, 613815, -2990680, 14730714, -73229290, 366936232, -1851352819, 9397497759, -47957377933, 245903408245, -1266266092111, 6545667052321, -33954266444497, 176689391245147, -922112642288148, 4825154135801698
OFFSET
0,2
FORMULA
G.f.: A(x) = -2*x*(1-x) / (1-sqrt(1+4*x*(1-x)^2)).
a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(2*k-1,k) * binomial(2*k-1,n-k)/(2*k-1).
MATHEMATICA
A366356[n_]:=(-1)^(n-1)Sum[Binomial[2k-1, k]Binomial[2k-1, n-k]/(2k-1), {k, 0, n}];
Array[A366356, 30, 0] (* Paolo Xausa, Oct 20 2023 *)
PROG
(PARI) a(n) = (-1)^(n-1)*sum(k=0, n, binomial(2*k-1, k)*binomial(2*k-1, n-k)/(2*k-1));
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Oct 08 2023
STATUS
approved