A099240 Main diagonal of A099239.

1, 2, 8, 41, 250, 1757, 13917, 122166, 1173662, 12222605, 136927351, 1639768418, 20880556880, 281460326864, 4000651782511, 59761935358025, 935445106491702, 15303039199768237, 261030618751031385, 4632889302298054713

Offset: 0

Author

Paul Barry, Oct 08 2004

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..490

Crossrefs

Cf. A099239.

Programs

Magma

[1] cat [(&+[Binomial(n+(n-1)*(j+1), n*(j+1)-1): j in [0..n]]): n in [1..30]]; // G. C. Greubel, Mar 09 2021

Mathematica

Table[Sum[Binomial[n^2 -(n-1)*(j-1), j], {j,0,n}], {n,0,30}] (* G. C. Greubel, Mar 09 2021 *)

Sage

[sum(binomial(n^2 -(n-1)*(j-1), j) for j in (0..n)) for n in (0..30)] # G. C. Greubel, Mar 09 2021

Formula

a(n) = Sum_{j=0..n} binomial(n^2 - (n-1)*(j-1), j).

a(n) = Sum_{j=0..n} binomial(n + (n-1)*(j+1), n*(j+1) - 1) with a(0) = 1.