A130563 Fourth column (m=3) of the Laguerre-Sonin a=1/2 coefficient triangle.

1, 36, 990, 25740, 675675, 18378360, 523783260, 15713497800, 496939367925, 16564645597500, 581419060472250, 21459648959248500, 831561397170879375, 33774185977401870000, 1435402904039579475000, 63731888939357328690000

Offset: 3

Author

Wolfdieter Lang, Jul 13 2007

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 3..400

Crossrefs

Columns m=0, 1, 2 from A001147, A000457, A001881.

Eighth right hand column of triangle A001498. - Johannes W. Meijer, Oct 16 2009

Programs

Magma

[Round(Factorial(n)*2^(n-3)*Gamma(n+3/2)/(6*Gamma(n-2)*Gamma(9/2))): n in [3..20]]; // G. C. Greubel, May 12 2018

Mathematica

Table[n!*(2^(n - 3))*Binomial[n + 1/2, n - 3]/3!, {n, 3, 50}] (* G. C. Greubel, May 12 2018 *)

PARI

for(n=3, 20, print1(n!*(2^(n-3))*binomial(n+1/2, n-3)/3!, ", ")) \\ G. C. Greubel, May 12 2018

Formula

a(n) = n!*(2^(n-3))*binomial(n+1/2,n-3)/3!, n >= 3.

a(n) = binomial(n,3)*(2*n+1)!!/7!!, with (2*n+1)!! = A001147(n+1).

a(n) = -A130757(n,3), n >= 3.