A158194 a(n) = Sum_{i=1..n-1} (-1)^i*binomial(n, i-1)*binomial(n, i)*binomial(n, i+1).

0, -2, 0, 48, 0, -1080, 0, 24640, 0, -573300, 0, 13571712, 0, -325909584, 0, 7918859520, 0, -194292083700, 0, 4806057828000, 0, -119708452543680, 0, 2999393069557248, 0, -75538616795314400, 0, 1910952839165529600, 0

Offset

1,2

Links

Indranil Ghosh, Table of n, a(n) for n = 1..400

Matjaz Konvalinka, An inverse matrix formula in the right-quantum algebra, Electron. J. Combin., vol. 15 (1) (2008), Article R23.

Formula

a(2*n) = 2*(-1)^n*binomial(2*n, n-1)*binomial(3*n, n-1) with a(2*n-1) = 0.

Mathematica

Table[Sum[(-1)^i*Binomial[n, i-1]*Binomial[n, i]*Binomial[n, i+1], {i, n-1}], {n, 30}]

Prog

(Magma)
A158194:= func< n | n eq 1 select 0 else (&+[(-1)^j*Binomial(n, j-1)*Binomial(n, j)*Binomial(n, j+1): j in [1..n-1]]) >;
[A158194(n): n in [1..30]]; // G. C. Greubel, Jun 26 2021
(Sage)
def A158194(n): return 0 if (n%2==1) else 2*(-1)^(n/2)*binomial(n, n/2 -1)*binomial(3*n/2, n/2 -1)
[A158194(n) for n in (1..30)] # G. C. Greubel, Jun 26 2021

Crossrefs

Sequence in context: A303491 A303396 A319113 * A326718 A097173 A009493

Adjacent sequences: A158191 A158192 A158193 * A158195 A158196 A158197

Keyword

sign,easy

Author

Roger L. Bagula, Mar 13 2009

Extensions

Edited by the Associate Editors of the OEIS, Apr 22 2009

Status

approved