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A287596 a(n) is the denominator of r(n), where r(n) = r(n-1) + r(n-2)/(2*(n-1)) with r(0) = 0, r(1) = 1.

%I A287596 #12 Jun 08 2017 17:08:23
%S A287596 1,1,1,4,12,96,480,5760,8064,645120,5806080,116121600,1277337600,
%T A287596 6131220480,398529331200,11158821273600,167382319104000,
%U A287596 5356234211328000,18211196318515200,3278015337332736000,62282291409321984000,146546568021934080000,52317124783830466560000
%N A287596 a(n) is the denominator of r(n), where r(n) = r(n-1) + r(n-2)/(2*(n-1)) with r(0) = 0, r(1) = 1.
%C A287596 The numerators are in A286307.
%C A287596 From _Wolfdieter Lang_, Jun 07 2017: (Start)
%C A287596 According to a _Benoit Cloitre_ Aug 14 2003 formula in A019609 lim_{n-> oo} 4*n/r(n-1)^2 = Pi*e.
%C A287596 r(n+1) seems to be A268363(n) = 2^floor(n/2) * n!, n >= 0, up to n = 7, 12, 17, 20, 22, 27, 31, 32, 34,... (End)
%F A287596 a(n) = denominator(r(n)), where r(n) = r(n-1) + r(n-2)/2*(n-2) with r(0)=0 and r(1)=1.
%F A287596 G.f. of {r(n)}_{n>=0}: x*exp(-x/2)/(1-x)^(3/2). - _Wolfdieter Lang_, Jun 07 2017
%t A287596 Denominator[RecurrenceTable[{r[n] == r[n - 1] + r[n - 2]/(2 (n - 1)), r[0] == 0, r[1] == 1}, r, {n, 0, 22}]]
%o A287596 (PARI)
%o A287596 a(n) = if(n < 2, return(n)); n++; my(v=vector(n)); v[1]=0; v[2] = 1; for(i = 3, n, v[i] = v[i-1] + v[i-2]/(2*i - 4)); denominator(v[#v])
%Y A287596 Cf. A019609, A268363, A286307.
%K A287596 nonn,easy
%O A287596 0,4
%A A287596 _Terry D. Grant_, May 27 2017