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%I #12 Jan 02 2020 04:58:04
%S 2,2,34,84,1308,5424,89136,528480,9442080,73388160,1433047680,
%T 13835646720,294712992000,3407733504000,78854259456000,
%U 1063689242112000,26612469305856000,410604285708288000,11055592008050688000,192132082005405696000,5543038613901938688000
%N a(n) = (n+2)!(1/3 - 1/4 + ... + c/(n+2)), where c=(-1)^(n+1).
%H Andrew Howroyd, <a href="/A024176/b024176.txt">Table of n, a(n) for n = 1..100</a>
%F a(n) = 2*A024188(n).
%F a(n) ~ sqrt(2*Pi) * (log(2) - 1/2) * n^(n + 5/2) / exp(n). - _Vaclav Kotesovec_, Jan 02 2020
%t Table[(n+2)! * Sum[(-1)^(k+1)/k, {k, 3, n+2}], {n, 1, 25}] (* _Vaclav Kotesovec_, Jan 02 2020 *)
%o (PARI) a(n) = (n+2)!*sum(x=1, n, (-1)^(x+1)/(x+2)); \\ _Michel Marcus_, Mar 21 2013
%Y Cf. A024188.
%K nonn
%O 1,1
%A _Clark Kimberling_
%E Terms a(13) and beyond from _Andrew Howroyd_, Jan 01 2020
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