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%I #6 Oct 21 2023 06:21:59
%S 1,6,113400,32901422400,67651716132000000,608762379843757339200000,
%T 17903325789347617610786995200000,
%U 1415199921956087613201896962521600000000,261375521452474271183649591888039276441600000000,101519644940256627137917269623207295713536128000000000000,76392226231236455854222646891536244623780022885776896000000000000
%N Let f(M,N)=2^(-M)*sum_{i=0..N} {(-1)^{i}M!N!(2M-2i)!}/{i!(M-i)!(N-i)!6^{N-i}}; then a(n) = f(3n,n).
%F a(n) ~ sqrt(Pi) * 2^(2*n+1) * 3^(5*n + 1/2) * n^(6*n + 1/2) / exp(6*n + 1/2). - _Vaclav Kotesovec_, Oct 21 2023
%t Table[2^(-3*n) * Sum[(-1)^i * (3*n)! * n! * (6*n-2*i)! / (i! * (3*n-i)! * (n-i)! * 6^(n-i)), {i,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Oct 21 2023 *)
%t Table[(6*n)! * Hypergeometric1F1[-n, 1/2 - 3*n, -3/2] / (2^(4*n) * 3^n), {n, 0, 20}] (* _Vaclav Kotesovec_, Oct 21 2023 *)
%Y A variant of A132202. Cf. A134648, A134772, A152296.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Oct 18 2009
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