login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A130189 Numerators of z-sequence for the Sheffer matrix (triangle) A094816 (coefficients of Poisson-Charlier 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
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_{j=0..n-1} z(j)*S(n-1,j), n >= 1, S(0,0)=1.
See the W. Lang link under A006232 with a summary on a- and z-sequences for Sheffer matrices.
LINKS
FORMULA
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). - 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); # Peter Luschny, Apr 28 2009
MATHEMATICA
Table[(-1)^n*Numerator[Sum[StirlingS2[n, k]/(k + 1), {k, 0, n}]], {n, 0, 50}] (* G. C. Greubel, Jul 10 2018 *)
PROG
(PARI) a(n) = (-1)^n*numerator(sum(k=0, n, stirling(n, k, 2)/(k+1))); \\ Michel Marcus, Jan 15 2015
CROSSREFS
Cf. A027641/A027642 (Bernoulli numbers) provide the a-sequence for the Sheffer matrix A094816.
Sequence in context: A307361 A260829 A355970 * A180755 A073624 A025546
KEYWORD
sign,frac,easy
AUTHOR
Wolfdieter Lang, Jun 01 2007
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)