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%I #7 Oct 30 2017 07:12:36
%S 0,1,-2,4,-6,11,-14,29,-26,85,-12,320,312,1639,3190,10484,25822,75005,
%T 200488,564662,1555804,4363139,12184456,34267931,96435100,272390561,
%U 770734846,2186278294,6213111234
%N Inverse binomial transform of A000957.
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F From _Vaclav Kotesovec_, Oct 30 2017: (Start)
%F Recurrence: 2*n*a(n) = -(n+6)*a(n-1) + (13*n - 33)*a(n-2) + 3*(7*n - 18)*a(n-3) + 9*(n-3)*a(n-4).
%F a(n) ~ 3^(n - 1/2) / (8 * sqrt(Pi) * n^(3/2)). (End)
%t Table[Sum[(-1)^(n-k) * Binomial[n, k]*(2^k * (2*k-1)!! * Hypergeometric2F1Regularized[2, 2*k+1, k+2, -1] - 3*(-1)^k/2^(k+1)), {k, 1, n}], {n, 0, 30}] (* _Vaclav Kotesovec_, Oct 30 2017 *)
%Y Cf. A000957, A138415.
%K sign
%O 0,3
%A _N. J. A. Sloane_, May 08 2008