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A329495
Numerator of second moment of the n-th term of Ulam's "history-dependent random sequence".
4
1, 4, 25, 101, 655, 11077, 94199, 2005319, 62541113, 530615357, 3888615949, 2547768661, 1603125774433, 510235838011, 76538488318091, 10462945272539099, 182249306891497151, 7488308007918913129, 6810487755999748187
OFFSET
1,2
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.
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
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Nov 17 2019
STATUS
approved