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%I #12 Jan 02 2020 04:07:18
%S 2,6,146,1164,32108,432720,14141360,271332960,10373558240,
%T 259311694080,11400458720000,351858201408000,17517836995904000,
%U 644027147554560000,35846613866733824000,1530195810548224512000,94207122098479233536000,4580941398125400354816000
%N a(n) = s(1)*s(2)*...*s(n+1)*(1/s(2) - 1/s(3) + ... + c/s(n+1)), where c = (-1)^(n+1) and s(k) = 3k-1 for k = 1,2,3,...
%H Andrew Howroyd, <a href="/A024397/b024397.txt">Table of n, a(n) for n = 1..100</a>
%F a(n) ~ Gamma(1/3) * (9 - 2*Pi*sqrt(3) + 6*log(2)) * 3^(n - 1/2) * n^(n + 7/6) / (2^(3/2) * sqrt(Pi) * exp(n)). - _Vaclav Kotesovec_, Jan 02 2020
%t Table[Product[3*k - 1, {k, 1, n+1}] * Sum[(-1)^k/(3*k - 1), {k, 2, n+1}], {n, 1, 20}] (* _Vaclav Kotesovec_, Jan 02 2020 *)
%o (PARI) a(n)={my(s=vector(n+1, k, 3*k-1)); vecprod(s)*sum(k=2, #s, (-1)^k/s[k])} \\ _Andrew Howroyd_, Jan 01 2020
%Y Cf. A024218, A024384.
%K nonn
%O 1,1
%A _Clark Kimberling_
%E Terms a(11) and beyond from _Andrew Howroyd_, Jan 01 2020
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