A177788 a(n) = binomial(n^2, n+1)/(n-1).

4, 63, 1456, 44275, 1669536, 75163011, 3934369216, 234799050915, 15736644960400, 1170354134607658, 95648578915114512, 8520904136405458044, 821828481957792579648, 85317719822978885714475, 9485883860726883646713600, 1124586875214241546178986915

Offset: 2

Author

Michel Lagneau, May 13 2010

Keywords

• nonn

Comments

The entries are integer for n >= 2 because binomial(n^2,n+1)/(n-1) = n*binomial(n^2-2,n-1), which is a product of two integers.

Links

• G. C. Greubel, Table of n, a(n) for n = 2..335

Crossrefs

Cf. A000108, A014062, A060545, A177234, A177456, A177784.

Programs

Magma

[Binomial(n^2,n+1)/(n-1): n in [2..30]]; // G. C. Greubel, Apr 28 2024

Maple

n0:=30: T:=array(1..n0): T:=array(1..n0-1): for n from 2 to n0 do: T[n-1]:= (binomial(n^2,n+1))/(n-1): od: print(T):

Mathematica

Table[Binomial[n^2,n+1]/(n-1), {n,2,40}] (* G. C. Greubel, Apr 28 2024 *)

PARI

a(n) = binomial(n^2, n+1)/(n-1) \\ Charles R Greathouse IV, May 01 2024

SageMath

[binomial(n^2,n+1)/(n-1) for n in range(2,31)] # G. C. Greubel, Apr 28 2024

Formula

a(n) = binomial(n^2,n+1)/(n-1).

a(n) = n * A177234(n).

a(n) = n^2 * A177784(n).

Extensions

Removed redundant second Maple version - R. J. Mathar, May 14 2010