A342295 a(n) = Sum_{k = 0..n} binomial(n,k)^12.

1, 2, 4098, 1062884, 2210336770, 2000488281252, 4355497029345924, 6773152698818628936, 15744083665278445490178, 32270900877696351763796420, 80314784333143089874093429348, 192454957455454582636391397662856, 509571049488109525160616367158261124

Offset: 0

Author

N. J. A. Sloane, Mar 27 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..281
• M. A. Perlstadt, Some Recurrences for Sums of Powers of Binomial Coefficients, Journal of Number Theory 27 (1987), pp. 304-309.

Crossrefs

Column 12 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

PARI

a(n) = sum(k=0, n, binomial(n, k)^12); \\ 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=12. - Vaclav Kotesovec, Aug 04 2022