A180170 a(0) = 1, a(n) = n*a(n-1)*A014963(n).

1, 1, 4, 36, 288, 7200, 43200, 2116800, 33868800, 914457600, 9144576000, 1106493696000, 13277924352000, 2243969215488000, 31415569016832000, 471233535252480000, 15079473128079360000, 4357967734014935040000, 78443419212268830720000

Offset

0,3

Comments

Lcm of the first n terms of the sequence of the denominators A_n of the preprint.

Links

Table of n, a(n) for n=0..18.

L. A. Medina, V. H. Moll, E. S. Rowland, Iterated primitives of logarithmic powers, arXiv:0911.1325 [math.NT], 2009-2010, eq (1.6).

Jim Pitman and Wenpin Tang, Regenerative random permutations of integers, arXiv:1704.01166, [math.PR], 2017, p. 18.

Formula

a(n) = n! * lcm(1,2,...,n) = n! * A003418(n), n > 0. - Benedict W. J. Irwin, Nov 01 2016

Mathematica

(* First run the program for A014963 *) b[0] := 1; b[1] := 1; b[n_] := n * b[n - 1] * a[n]; Table[b[n], {n, 0, 19}] (* Alonso del Arte, Jan 16 2011 *)
Join[{1}, Table[n!LCM@@Range[n], {n, 1, 20}]] (* Benedict W. J. Irwin, Nov 01 2016 *)
F=Table[1, {n, 1, 20}]; For[i=1, i<20, i++, F[[i+1]]=(i+1)*F[[i]]*Exp[MangoldtLambda[i+1]]]; Join[{1}, F] (* Benedict W. J. Irwin, Nov 01 2016 *)

Prog

(PARI)
A014963(n)=
{
    local(r);
    if( isprime(n), return(n));
    if( ispower(n, , &r) && isprime(r), return(r) );
    return(1);
}
a(n)=if(n==0, 1, n * a(n-1) * A014963(n));
for(n=0, 55, print1(a(n), ", "))
/* Joerg Arndt, Jan 16 2011 */

Crossrefs

Sequence in context: A354401 A354404 A316297 * A277174 A059416 A240889

Adjacent sequences: A180167 A180168 A180169 * A180171 A180172 A180173

Keyword

nonn,easy

Author

R. J. Mathar, Jan 16 2011

Status

approved