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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A132364 Expansion of 1/(1-x^2*c(x)), c(x) the g.f. of A000108 . 6
1, 0, 1, 1, 3, 7, 20, 59, 184, 593, 1964, 6642, 22845, 79667, 281037, 1001092, 3595865, 13009673, 47366251, 173415176, 638044203, 2357941142, 8748646386, 32576869203, 121701491701, 456012458965, 1713339737086 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Diagonal sums of A106566 .

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

P. Barry, A note on Krawtchouk Polynomials and Riordan Arrays, JIS 11 (2008) 08.2.2

FORMULA

a(0)=1, a(n) = Sum_{k=0..floor(n/2)} (k/(n-k))*C(2n-3k-1,n-2k)), n>0 .

G.f.: (2-x-x*sqrt(1-4*x))/(2-2*x+2*x^3). - Philippe Deléham, Feb 24 2013

Conjecture: +(-n+1)*a(n) +(5*n-11)*a(n-1) +2*(-2*n+5)*a(n-2) +(-n+1)*a(n-3) +2*(2*n-5)*a(n-4)=0. - R. J. Mathar, Aug 28 2015

MATHEMATICA

a[0] := 1; a[n_] := Sum[(k/(n - k))*Binomial[2*n - 3*k - 1, n - 2*k], {k, 0, Floor[n/2]}]; Table[a[n], {n, 0, 25}] (* G. C. Greubel, Oct 19 2016 *)

CROSSREFS

Cf. A030238.

Sequence in context: A129429 A084204 A030238 * A110490 A132868 A056783

Adjacent sequences:  A132361 A132362 A132363 * A132365 A132366 A132367

KEYWORD

nonn

AUTHOR

Philippe Deléham, Nov 08 2007

EXTENSIONS

Typo in a(n) term corrected Johannes W. Meijer, Sep 13 2010

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 February 24 12:59 EST 2018. Contains 299623 sequences. (Running on oeis4.)