A329498 Denominator of the rational number alpha_n involved in the calculation of the second moment of the n-th term of Ulam's "history-dependent random sequence".

1, 1, 2, 6, 24, 120, 720, 1680, 40320, 362880, 725760, 7983360, 2128896, 113218560, 387459072, 261534873600, 836911595520, 71137485619200, 75322043596800, 1621934672117760, 37429261664256000, 10218188434341888000, 224800145555521536000

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

0, 2, 21/2, 223/6, 2603/24, 33623/120, 477977/720, 2474153/1680, ...

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, A329496, A327497.

Sequence in context: A232983 A319207 A263749 * A000805 A263750 A263751

Adjacent sequences: A329495 A329496 A329497 * A329499 A329500 A329501

Keyword

nonn,frac

Author

N. J. A. Sloane, Nov 17 2019

Status

approved