A138461 Inverse binomial transform of A000957.

0, 1, -2, 4, -6, 11, -14, 29, -26, 85, -12, 320, 312, 1639, 3190, 10484, 25822, 75005, 200488, 564662, 1555804, 4363139, 12184456, 34267931, 96435100, 272390561, 770734846, 2186278294, 6213111234

Offset

0,3

Links

Table of n, a(n) for n=0..28.

N. J. A. Sloane, Transforms

Formula

From Vaclav Kotesovec, Oct 30 2017: (Start)

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).

a(n) ~ 3^(n - 1/2) / (8 * sqrt(Pi) * n^(3/2)). (End)

Mathematica

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 *)

Crossrefs

Cf. A000957, A138415.

Sequence in context: A156913 A238483 A238487 * A173397 A187492 A366127

Adjacent sequences: A138458 A138459 A138460 * A138462 A138463 A138464

Keyword

sign

Author

N. J. A. Sloane, May 08 2008

Status

approved