Search: id:A130189
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%I A130189
%S A130189 1,1,5,7,68,167,2057,4637,75703,39941,676360,902547,602501827,432761746,
%T A130189 2438757091,8997865117,346824403906,1857709421899,325976550837563,282728710837871,
%U A130189 39928855264303811,16874802689368067,162083496666375118,3212329557624761759
%V A130189 1,-1,5,-7,68,-167,2057,-4637,75703,-39941,676360,-902547,602501827,-432761746,
%W A130189 2438757091,-8997865117,346824403906,-1857709421899,325976550837563,-282728710837871,
%X A130189 39928855264303811,-16874802689368067,162083496666375118,-3212329557624761759
%N A130189 Numerators of z-sequence for the Sheffer matrix (triangle) A094816 (coefficients 
               of Poisson-Charlier polynomials).
%C A130189 The denominators are given in A130190.
%C A130189 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.
%C A130189 See the W. Lang link under A006232 with a summary on a- and z-sequences 
               for Sheffer matrices.
%H A130189 W. Lang, <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A130189.text">
               Rationals, z-sequence. </a>
%F A130189 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).
%F A130189 Numerator of (-1)^n Sum_{k=0..n} A048993(n,k)/(k+1). [From Peter Luschny 
               (peter(AT)luschny.de), Apr 28 2009]
%e A130189 Rationals z(n): [1,-1/2,5/6,-7/4,68/15,-167/12,2057/42,-4637/24,....].
%e A130189 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.
%p A130189 seq(numer((-1)^n*add(stirling2(n,k)/(k+1),k=0..n)),n=0..20); [From Peter 
               Luschny (peter(AT)luschny.de), Apr 28 2009]
%Y A130189 Cf. A027641/A027642 (Bernoulli numbers) provide the a-sequence for the 
               Sheffer matrix A094816.
%Y A130189 Sequence in context: A106112 A108200 A077780 this_sequence A073624 A025546 
               A109715
%Y A130189 Adjacent sequences: A130186 A130187 A130188 this_sequence A130190 A130191 
               A130192
%K A130189 sign,frac,easy
%O A130189 0,3
%A A130189 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jun 01 2007

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