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URL: https://oeis.org/A287596

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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.
1
1, 1, 1, 4, 12, 96, 480, 5760, 8064, 645120, 5806080, 116121600, 1277337600, 6131220480, 398529331200, 11158821273600, 167382319104000, 5356234211328000, 18211196318515200, 3278015337332736000, 62282291409321984000, 146546568021934080000, 52317124783830466560000
OFFSET
0,4
COMMENTS
The numerators are in A286307.
From Wolfdieter Lang, Jun 07 2017: (Start)
According to a Benoit Cloitre Aug 14 2003 formula in A019609 lim_{n-> oo} 4*n/r(n-1)^2 = Pi*e.
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)
FORMULA
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.
G.f. of {r(n)}_{n>=0}: x*exp(-x/2)/(1-x)^(3/2). - Wolfdieter Lang, Jun 07 2017
MATHEMATICA
Denominator[RecurrenceTable[{r[n] == r[n - 1] + r[n - 2]/(2 (n - 1)), r[0] == 0, r[1] == 1}, r, {n, 0, 22}]]
PROG
(PARI)
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])
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Terry D. Grant, May 27 2017
STATUS
approved