login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A184881 a(n) = A184879(2*n, n) - A184879(2*n, n+1) where A184879(n, k) = Hypergeometric2F1(-2*k, 2*k-2*n, 1, -1) if 0<=k<=n. 3
1, -3, 2, -3, 6, -14, 36, -99, 286, -858, 2652, -8398, 27132, -89148, 297160, -1002915, 3421710, -11785890, 40940460, -143291610, 504932340, -1790214660, 6382504440, -22870640910, 82334307276, -297670187844, 1080432533656 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Hankel transform is A184882.

Signed version of A007054. - Philippe Deléham, Mar 19 2014

LINKS

Table of n, a(n) for n=0..26.

J. W. Layman, The Hankel Transform and Some of Its Properties, J. Integer Sequences 4, No. 01.1.5, 2001

Fumitaka Yura, Hankel Determinant Solution for Elliptic Sequence, arXiv:1411.6972 [nlin.SI], (25-November-2014); see p. 7

FORMULA

a(n) = 0^n + Sum_{k=0..2n} (C(2n,k)^2-C(2n+2,k)*C(2n-2,k))*(-1)^k.

G.f.: (8*x+1-sqrt(1+4*x)^3)/(2*x). - Philippe Deléham, Mar 19 2014

a(0) = 1, a(n) = (-1)^n*A007054(n-1) for n>0. - Philippe Deléham, Mar 19 2014

(n+1)*a(n) +2*(2*n-3)*a(n-1)=0. - R. J. Mathar, Nov 19 2014

EXAMPLE

a(0) = 1;

a(1) = 1 - 4*1 = -3;

a(2) = 4*1 - 2 = 2;

a(3) = 5 - 4*2 = -3;

a(4) = 4*5 - 14 = 6;

a(5) = 42 - 4*14 = -14;

a(6) = 4*42 - 132 = 36;

a(7) = 429 - 4*132 = -99;

a(8) = 4*429 - 1430 = 286, etc; with A000108 = 1,1,2,5,14,42,132,429,1430, ... - Philippe Deléham, Mar 19 2014

MAPLE

A184879 := proc(n, k) if k<0 or k >n then 0; else hypergeom([-2*k, 2*k-2*n], [1], -1) ; simplify(%) ; end if; end proc:

A184881 := proc(n) A184879(2*n, n)-A184879(2*n, n+1) ; end proc:

seq(A184881(n), n=0..40) ; # R. J. Mathar, Feb 05 2011

MATHEMATICA

h[n_, k_] := HypergeometricPFQ[{-2k, 2k - 2n}, {1}, -1];

a[0] = 1; a[n_] := h[2n, n] - h[2n, n + 1];

Table[a[n], {n, 0, 26}] (* Jean-François Alcover, Nov 24 2017 *)

CROSSREFS

Cf. A000108, A007054, A184879, A184882.

Sequence in context: A215413 A058644 A049923 * A007054 A084388 A136389

Adjacent sequences:  A184878 A184879 A184880 * A184882 A184883 A184884

KEYWORD

sign

AUTHOR

Paul Barry, Jan 24 2011

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 April 3 22:48 EDT 2020. Contains 333207 sequences. (Running on oeis4.)