A226391 a(n) = Sum_{k=0..n} binomial(k*n, k).

1, 2, 9, 103, 2073, 58481, 2101813, 91492906, 4671050401, 273437232283, 18046800575211, 1325445408799007, 107200425419863009, 9466283137384124247, 906151826270369213655, 93459630239922214535911, 10331984296666203358431361, 1218745075041575200343722415

Offset: 0

Author

Vaclav Kotesovec, Jun 06 2013

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A072034, A086331, A096131, A167008, A167010, A349471.

Programs

Magma

[(&+[Binomial(n*j,j): j in [0..n]]): n in [0..30]]; // G. C. Greubel, Aug 31 2022

Mathematica

Table[Sum[Binomial[k*n, k], {k, 0, n}], {n, 0, 20}]

Maxima

A226391(n):=sum(binomial(k*n,k), k,0,n); makelist(A226391(n),n,0,30); /* Martin Ettl, Jun 06 2013 */

SageMath

@CachedFunction
def A226391(n): return sum(binomial(n*j, j) for j in (0..n))
[A226391(n) for n in (0..30)] # G. C. Greubel, Aug 31 2022

Formula

a(n) ~ binomial(n^2, n).