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, 4, 12, 96, 480, 5760, 8064, 645120, 5806080, 116121600, 1277337600, 6131220480, 398529331200, 11158821273600, 167382319104000, 5356234211328000, 18211196318515200, 3278015337332736000, 62282291409321984000, 146546568021934080000, 52317124783830466560000

Offset: 0

Author

Terry D. Grant, May 27 2017

Keywords

• nonn
• easy

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)

Crossrefs

Cf. A019609, A268363, A286307.

Programs

Mathematica

Denominator[RecurrenceTable[{r[n] == r[n - 1] + r[n - 2]/(2 (n - 1)), r[0] == 0, r[1] == 1}, r, {n, 0, 22}]]

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])

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