

A130190


Denominators of zsequence for the Sheffer matrix (triangle) A094816 (coefficients of PoissonCharlier polynomials).


4



1, 2, 6, 4, 15, 12, 42, 24, 90, 10, 33, 8, 910, 105, 90, 48, 255, 180, 3990, 420, 6930, 330, 345, 720, 13650, 273, 378, 28, 145, 20, 14322, 2464, 117810, 3570, 7, 24, 1919190, 1729, 2730, 840, 9471, 13860, 99330, 1540, 217350, 4830, 4935, 10080, 324870
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OFFSET

0,2


COMMENTS

The numerators are given in A130189.
See A130189 for the W. Lang link on zsequences for Sheffer matrices.
The prime factors of each a(n) are such that n!/a(n) has the prime, p = n+1, as the denominator of its reduced fraction, and if n+1 is not prime then n!/a(n) is an integer, except at n = 3, which has denominator = 2. Also see alternate formula for a(n) below.  Richard R. Forberg, Dec 28 2014
As implied above, at n = p1 the largest prime factor of a(n) is p. For a(m), where m is an integer within the set given by A089965, the two largest prime factors of a(m) are m+1 and (m+1)/2. Furthermore, it appears, when n+1 is not a prime no prime factor of a(n) is greater than k/2, where k is the next higher value of n where n+1 is prime. Two examples at this upper limit of k/2 are n = 104 and 105, where the highest prime factor of a(n) is 53; it is then at n = k = 106 where n+1 is prime.  Richard R. Forberg, Jan 01 2015


LINKS

Table of n, a(n) for n=0..48.


FORMULA

a(n) = denominator(z(n)),n>=0, with the e.g.f. for z(n) given in A130189.
Denominator of Sum_{k=0..n} A048993(n,k)/(k+1). [Peter Luschny, Apr 28 2009]
Alternate: a(n) = denominator((1/e)*Sum_{k>=0}*(Sum_{j=0..k} j^n/k!)). NOTE: Numerators are different from A130189, and given by A248716.  Richard R. Forberg, Dec 28 2014
This more generalized expression ((1/e)*Sum_{k>=0} (Sum_{j=0..k} (j+m)^n/k!)), gives the same denominators for any integer m.  Richard R. Forberg, Jan 14 2015


MAPLE

seq(denom(add(stirling2(n, k)/(k+1), k=0..n)), n=0..20); # Peter Luschny, Apr 28 2009


MATHEMATICA

Denominator[Table[(1/Exp[1])* Sum[Sum[j^n/k!, {j, 0, k}], {k, 0, Infinity}],
{n, 0, 100}]] (* Richard R. Forberg, Dec 28 2014 *)


PROG

(PARI) a(n) = denominator(sum(k=0, n, stirling(n, k, 2)/(k+1))); \\ Michel Marcus, Jan 15 2015, after Maple


CROSSREFS

Cf. A089965, A094816, A248716, A130189.
Sequence in context: A111807 A069914 A200746 * A110346 A095754 A226718
Adjacent sequences: A130187 A130188 A130189 * A130191 A130192 A130193


KEYWORD

nonn,easy


AUTHOR

Wolfdieter Lang, Jun 01 2007


STATUS

approved



