|
%I #28 Sep 01 2022 05:00:52
%S 1,2,9,103,2073,58481,2101813,91492906,4671050401,273437232283,
%T 18046800575211,1325445408799007,107200425419863009,
%U 9466283137384124247,906151826270369213655,93459630239922214535911,10331984296666203358431361,1218745075041575200343722415
%N a(n) = Sum_{k=0..n} binomial(k*n, k).
%H Vincenzo Librandi, <a href="/A226391/b226391.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) ~ binomial(n^2, n).
%t Table[Sum[Binomial[k*n, k], {k, 0, n}], {n, 0, 20}]
%o (Maxima) A226391(n):=sum(binomial(k*n,k), k,0,n); makelist(A226391(n),n,0,30); /* _Martin Ettl_, Jun 06 2013 */
%o (Magma) [(&+[Binomial(n*j,j): j in [0..n]]): n in [0..30]]; // _G. C. Greubel_, Aug 31 2022
%o (SageMath)
%o @CachedFunction
%o def A226391(n): return sum(binomial(n*j, j) for j in (0..n))
%o [A226391(n) for n in (0..30)] # _G. C. Greubel_, Aug 31 2022
%Y Cf. A072034, A086331, A096131, A167008, A167010, A349471.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Jun 06 2013
|
