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

1,3

Links

Table of n, a(n) for n=1..23.

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.

Example

1, 4, 25/2, 101/3, 655/8, 11077/60, 94199/240, 2005319/2520, ...

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

Crossrefs

Cf. A329495, A329497, A327498.

Sequence in context: A292893 A356902 A042365 * A160634 A072043 A347289

Adjacent sequences: A329493 A329494 A329495 * A329497 A329498 A329499

Keyword

nonn,frac

Author

N. J. A. Sloane, Nov 17 2019

Status

approved