A342294 a(n) = Sum_{k = 0..n} binomial(n,k)^11.

1, 2, 2050, 354296, 371185666, 200097656252, 222100237312864, 193798873701831680, 231719476114879600642, 257097895846251291074612, 330463219813679264204224300, 419460465362069257397304825200, 573863850341313751827291703127200

Offset: 0

Author

N. J. A. Sloane, Mar 27 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..306
• M. A. Perlstadt, Some Recurrences for Sums of Powers of Binomial Coefficients, Journal of Number Theory 27 (1987), pp. 304-309.

Crossrefs

Column 11 of A309010.

Sum_{k = 0..n} C(n,k)^m for m = 1..12: A000079, A000984, A000172, A005260, A005261, A069865, A182421, A182422, A182446, A182447, A342294, A342295.

Programs

Mathematica

Table[Sum[Binomial[n,k]^11,{k,0,n}],{n,0,15}] (* Harvey P. Dale, May 08 2025 *)

PARI

a(n) = sum(k=0, n, binomial(n, k)^11); \\ Michel Marcus, Mar 27 2021

Formula

a(n) ~ 2^(p*n)/sqrt(p) * (2/(Pi*n))^((p-1)/2) * (1 - (p-1)^2/(4*p*n)), set p=11. - Vaclav Kotesovec, Aug 04 2022