

A130189


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


4



1, 1, 5, 7, 68, 167, 2057, 4637, 75703, 39941, 676360, 902547, 602501827, 432761746, 2438757091, 8997865117, 346824403906, 1857709421899, 325976550837563, 282728710837871, 39928855264303811, 16874802689368067, 162083496666375118, 3212329557624761759
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OFFSET

0,3


COMMENTS

The denominators are given in A130190.
This zsequence is useful for the recurrence for S(n,m=0):= A094816(n,0) (first column): S(n,0) = n*sum(z(j)*S(n1,j),j=0..n1). n>=1. S(0,0):=1.
See the W. Lang link under A006232 with a summary on a and zsequences for Sheffer matrices.


LINKS

Table of n, a(n) for n=0..23.
W. Lang, Rationals, zsequence.


FORMULA

E.g.f. for rationals z(n)=a(n)/A130190(n) (in lowest terms): (1exp(h(x)))/h(x) with h(x):=1exp(x).
Numerator of (1)^n Sum_{k=0..n} A048993(n,k)/(k+1). [From Peter Luschny, Apr 28 2009]


EXAMPLE

Rationals z(n): [1,1/2,5/6,7/4,68/15,167/12,2057/42,4637/24,....].
Recurrence from z(n) sequence for S(n,0):= A094816(n,0) for n=4: 1=S(4,0)=4*(1*1(1/2)*8+(5/6)*6(7/4)*1) with the 3rd row [1,8,6,1] of A094816.


MAPLE

seq(numer((1)^n*add(stirling2(n, k)/(k+1), k=0..n)), n=0..20); [From Peter Luschny, Apr 28 2009]


CROSSREFS

Cf. A027641/A027642 (Bernoulli numbers) provide the asequence for the Sheffer matrix A094816.
Sequence in context: A177336 A108200 A077780 * A180755 A073624 A025546
Adjacent sequences: A130186 A130187 A130188 * A130190 A130191 A130192


KEYWORD

sign,frac,easy


AUTHOR

Wolfdieter Lang Jun 01 2007


STATUS

approved



