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, 3956195377134000, 18712804133843820, 87835611240491400

Offset

0,2

Comments

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, Vol. L (2021), 36-43.

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

From R. J. Mathar, Aug 09 2015: (Start)

G.f.: 2F1(5/2,3;1;4x).

a(n) = A020920(n) + 12*A020920(n-1) + 6*A020920(n-2).

a(n) = (n+1)*A002803(n). (End)

a(n) ~ 2^(2*n+1) * n^(7/2) / (3 * sqrt(Pi)). - Amiram Eldar, Sep 21 2025

Mathematica

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

Crossrefs

Fifth column of A104684.

Cf. A007744, A002544, A002457.

Cf. A002803, A020920.

Sequence in context: A255002 A126922 A276287 * A097213 A110612 A290363

Adjacent sequences: A106437 A106438 A106439 * A106441 A106442 A106443

Keyword

easy,nonn

Author

Paul Barry, May 02 2005

Status

approved