A329496 Denominator of second moment of the n-th term of Ulam's "history-dependent random sequence".
1, 1, 2, 3, 8, 60, 240, 2520, 40320, 181440, 725760, 266112, 95800320, 17791488, 1585059840, 130767436800, 1394852659200, 35568742809600, 20324995891200, 12164510040883200, 69511485947904000, 5109094217170944000, 32114306507931648000
Offset: 1
Examples
1, 4, 25/2, 101/3, 655/8, 11077/60, 94199/240, 2005319/2520, ...
Links
- Mark Kac, A history-dependent random sequence defined by Ulam, Advances in Applied Mathematics 10.3 (1989): 270-277. See page 273, sigma_k and alpha_k.
Programs
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Maple
s:=[1]; a:=[0]; for N from 2 to 40 do # N = n+1 n:=N-1; t1:=s[n]+(1/n)*add(s[k],k=1..n)+2*s[n]/n+(2/n)*a[n]; t2:=s[n]+(1/n)*add(s[k],k=1..n)+a[n]+(2/n)*add(a[k],k=1..n); s:=[op(s),t1]; a:=[op(a),t2]; od: s; # sigma_n a; # alpha_n sn:=map(numer,s); # A329495 sd:=map(denom,s); # A329496 an:=map(numer,a); # A329497 ad:=map(denom,a); # A329498