login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A111884 E.g.f.: exp(x/(1+x)). 15
1, 1, -1, 1, 1, -19, 151, -1091, 7841, -56519, 396271, -2442439, 7701409, 145269541, -4833158329, 104056218421, -2002667085119, 37109187217649, -679877731030049, 12440309297451121, -227773259993414719, 4155839606711748061, -74724654677947488521, 1293162252850914402221 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Row sums of triangle A111596.

With different signs see A066668.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..450

P. Barry, The Restricted Toda Chain, Exponential Riordan Arrays, and Hankel Transforms, J. Int. Seq. 13 (2010) # 10.8.4, example 4.

P. Barry, Exponential Riordan Arrays and Permutation Enumeration, J. Int. Seq. 13 (2010) # 10.9.1, example 6.

P. Barry, Riordan Arrays, Orthogonal Polynomials as Moments, and Hankel Transforms, J. Int. Seq. 14 (2011) # 11.2.2, example 20.

P. Barry, Combinatorial Polynomials as Moments, Hankel Transforms, and Exponential Riordan Arrays, J. Int. Seq. 14 (2011)  11.6.7, example 10.

A. Hennessy, P. Barry, Generalized Stirling Numbers, Exponential Riordan Arrays, and Orthogonal Polynomials, J. Int. Seq. 14 (2011) # 11.8.2

FORMULA

E.g.f.: exp(x/(1+x)).

From Sergei N. Gladkovskii, Jul 21 2012: (Start)

Let E(x) be the e.g.f., then

E(x) = 1/G(0) where G(k)= 1 - x/((1+x)*(2*k+1) - x*(1+x)*(2*k+1)/(x - (1+x)*(2*k+2)/G(k+1))); (continued fraction, 3rd kind, 3-step).

E(x) = 1 + x/(G(0)-x) where G(k)= 1 + 2*x + (1+x)*k - x*(1+x)*(k+1)/G(k+1); (continued fraction, Euler's 1st kind, 1-step).

E(x) = G(0) where G(k)= 1 + x/((1+x)*(2*k+1) - x*(1+x)*(2*k+1)/(x + 2*(1+x)*(k+1)/G(k+1))); (continued fraction, 3rd kind, 3-step).

(End)

E.g.f.: 1 + x*(E(0)-1)/(x+1) where E(k) = 1 + 1/(k+1)/(1+x)/(1-x/(x+1/E(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jan 27 2013

E.g.f.: E(0)/2, where E(k)= 1 + 1/(1 - x/(x + (k+1)*(1+x)/E(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 31 2013

a(n) = sum(k=0..n, (-1)^(n-k)*L(n,k)); L(n,k) the unsigned Lah numbers. - Peter Luschny, Oct 18 2014

a(n) = hypergeom([-n+1,-n],[],-1). - Peter Luschny, Apr 08 2015

a(n) +(2*n-3)*a(n-1) +(n-1)*(n-2)*a(n-2)=0. - R. J. Mathar, Jul 20 2017

MATHEMATICA

nn=30; CoefficientList[Series[Exp[x/(1+x)], {x, 0, nn}], x] Range[0, nn]! (* Harvey P. Dale, Jul 21 2011 *)

PROG

(Sage)

A111884 = lambda n: hypergeometric([-n+1, -n], [], -1)

[Integer(A111884(n).n(100)) for n in (0..23)] # Peter Luschny, Sep 23 2014

CROSSREFS

Unsigned row sums of A111596: A000262.

Sequence in context: A125356 A293116 A066668 * A126514 A168025 A160431

Adjacent sequences:  A111881 A111882 A111883 * A111885 A111886 A111887

KEYWORD

sign,easy

AUTHOR

Wolfdieter Lang, Aug 23 2005

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified October 19 06:56 EDT 2017. Contains 293572 sequences.