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

0,2

Links

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

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.

Mathematica

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

Prog

(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
(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

Crossrefs

Cf. A099239.

Sequence in context: A177340 A067119 A093935 * A134055 A136281 A125698

Adjacent sequences: A099237 A099238 A099239 * A099241 A099242 A099243

Keyword

easy,nonn

Author

Paul Barry, Oct 08 2004

Status

approved