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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A103137 First column of inverse of Delannoy triangle. 5
1, -1, 2, -6, 22, -90, 394, -1806, 8558, -41586, 206098, -1037718, 5293446, -27297738, 142078746, -745387038, 3937603038, -20927156706, 111818026018, -600318853926, 3236724317174, -17518619320890, 95149655201962, -518431875418926, 2832923350929742, -15521467648875090 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

First column of A103136. The positive sequence has g.f. 1+xS(x). It is the first column of the inverse of the signed Delannoy triangle which has general term T(n,k)=if(k<=n, sum{j=0..k, 2^j*C(n-k,j)C(k,j)}(-1)^(n-k),0).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

G.f.: 1-xS(-x), where S(x) is the g.f. of the large Schroeder numbers A006318.

Conjecture: n*a(n) +3*(2*n-3)*a(n-1) +(n-3)*a(n-2)=0. - R. J. Mathar, Nov 26 2012

a(n) ~ (-1)^n * sqrt(3*sqrt(2)-4) * (3+2*sqrt(2))^n / (2*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Feb 13 2014

MATHEMATICA

CoefficientList[Series[1+x*(1+x-(1+6*x+x^2)^(1/2))/(2*x), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 13 2014 *)

CROSSREFS

A minor variation of A006318.

Sequence in context: A086456 A155069 A006318 * A165546 A279568 A053617

Adjacent sequences:  A103134 A103135 A103136 * A103138 A103139 A103140

KEYWORD

easy,sign

AUTHOR

Paul Barry, Jan 24 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 15 11:18 EST 2019. Contains 329144 sequences. (Running on oeis4.)