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%I #18 Aug 04 2022 03:28:36
%S 1,2,4098,1062884,2210336770,2000488281252,4355497029345924,
%T 6773152698818628936,15744083665278445490178,
%U 32270900877696351763796420,80314784333143089874093429348,192454957455454582636391397662856,509571049488109525160616367158261124
%N a(n) = Sum_{k = 0..n} binomial(n,k)^12.
%H Seiichi Manyama, <a href="/A342295/b342295.txt">Table of n, a(n) for n = 0..281</a>
%H M. A. Perlstadt, <a href="http://dx.doi.org/10.1016/0022-314X(87)90069-2">Some Recurrences for Sums of Powers of Binomial Coefficients</a>, Journal of Number Theory 27 (1987), pp. 304-309.
%F 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
%o (PARI) a(n) = sum(k=0, n, binomial(n, k)^12); \\ _Michel Marcus_, Mar 27 2021
%Y Column 12 of A309010.
%Y Sum_{k = 0..n} C(n,k)^m for m = 1..12: A000079, A000984, A000172, A005260, A005261, A069865, A182421, A182422, A182446, A182447, A342294, A342295.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Mar 27 2021
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