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A130189
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Numerators of z-sequence for the Sheffer matrix (triangle) A094816 (coefficients of Poisson-Charlier polynomials).
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4
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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
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0,3
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COMMENTS
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The denominators are given in A130190.
This z-sequence is useful for the recurrence for S(n,m=0):= A094816(n,0) (first column): S(n,0) = n*sum(z(j)*S(n-1,j),j=0..n-1). n>=1. S(0,0):=1.
See the W. Lang link under A006232 with a summary on a- and z-sequences for Sheffer matrices.
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LINKS
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Table of n, a(n) for n=0..23.
W. Lang, Rationals, z-sequence.
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FORMULA
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E.g.f. for rationals z(n)=a(n)/A130190(n) (in lowest terms): (1-exp(-h(x)))/h(x) with h(x):=1-exp(-x).
Numerator of (-1)^n Sum_{k=0..n} A048993(n,k)/(k+1). [From Peter Luschny, Apr 28 2009]
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EXAMPLE
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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.
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MAPLE
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seq(numer((-1)^n*add(stirling2(n, k)/(k+1), k=0..n)), n=0..20); [From Peter Luschny, Apr 28 2009]
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CROSSREFS
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Cf. A027641/A027642 (Bernoulli numbers) provide the a-sequence for the Sheffer matrix A094816.
Sequence in context: A177336 A108200 A077780 * A180755 A073624 A025546
Adjacent sequences: A130186 A130187 A130188 * A130190 A130191 A130192
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KEYWORD
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sign,frac,easy
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AUTHOR
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Wolfdieter Lang Jun 01 2007
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STATUS
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approved
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