A106440 a(n) = binomial(2n+4,n)*binomial(n+4,4).

1, 30, 420, 4200, 34650, 252252, 1681680, 10501920, 62355150, 355655300, 1963217256, 10546208400, 55367594100, 285028443000, 1442592936000, 7193730107520, 35406640372950, 172255143129300, 829376615067000

Offset: 0

Author

Paul Barry, May 02 2005

Keywords

• easy
• nonn

Comments

Fifth column of A104684.

Diagonal of the rational function 1 / (1 - x - y)^5. - Ilya Gutkovskiy, Apr 24 2025

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..1642
• Ömür Deveci and Anthony G. Shannon, Some aspects of Neyman triangles and Delannoy arrays, Mathematica Montisnigri (2021) Vol. L, 36-43.

Crossrefs

Cf. A007744, A002544, A002457.

Cf. A002803, A020920.

Programs

Mathematica

Table[Binomial[2n+4,n]Binomial[n+4,4],{n,0,20}] (* Harvey P. Dale, May 03 2019 *)

Formula

G.f.: (1+12x+6x^2)/(1-4x)^(9/2).

D-finite with recurrence n^2*a(n) -2*(n+2)*(2*n+3)*a(n-1)=0. - R. J. Mathar, Feb 20 2015

G.f.: 2F1(5/2,3;1;4x). - R. J. Mathar, Aug 09 2015

a(n) = A020920(n)+12*A020920(n-1)+6*A020920(n-2). - R. J. Mathar, Aug 09 2015

a(n) = (n+1)*A002803(n). - R. J. Mathar, Aug 09 2015