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 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 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

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