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%I #5 Dec 14 2019 19:24:09
%S 1,3,4,19,31,168,323,1859,4072,24403,59423,368488,980123,6275139,
%T 17998264,118858755,364059999,2478263856,8045642683,56418223739,
%U 192980878976,1392909382923,4995715059111,37083230363840,138896979832131,1059335618366171
%N a(n) = n * n!! - Sum_{k=1..n-1} k!! * a(n-k).
%C Logarithmic derivative of A006882.
%F L.g.f.: log(Sum_{k>=0} k!! * x^k).
%t a[n_] := a[n] = n n!! - Sum[k!! a[n - k], {k, 1, n - 1}]; Table[a[n], {n, 1, 26}]
%t nmax = 26; CoefficientList[Series[Log[Sum[k!! x^k, {k, 0, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Rest
%Y Cf. A003319, A004208, A006882, A233824, A307064.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Dec 14 2019
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