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 A098337 Expansion of 1/sqrt(1-4x+20x^2). 3
 1, 2, -4, -40, -80, 352, 2624, 3712, -32000, -186880, -134144, 2885632, 13520896, -1269760, -256000000, -966164480, 1056112640, 22286827520, 66722201600, -162411315200, -1901125959680, -4329895362560 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Central coefficients of (1+2x-4x^2)^n. Binomial transform of A098334. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Hacène Belbachir, Abdelghani Mehdaoui, László Szalay, Diagonal Sums in the Pascal Pyramid, II: Applications, J. Int. Seq., Vol. 22 (2019), Article 19.3.5. Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7. FORMULA E.g.f.: exp(2x)BesselI(0, 4*I*x), I=sqrt(-1); a(n) = sum{k=0..floor(n/2), binomial(n, k)binomial(n-k, k)2^n(-1)^k}; a(n) = sum{k=0..n, binomial(2k, k)binomial(k, n-k)(-5)^(n-k)}. a(n) = Sum_{k=0..floor(n/2)} binomial(n, k)binomial(2(n-k), n)(-5)^k. - Paul Barry, Sep 08 2004. D-finite with recurrence: n*a(n) +2*(-2*n+1)*a(n-1) +20*(n-1)*a(n-2)=0. - R. J. Mathar, Nov 24 2012 Lim sup n->infinity |a(n)|^(1/n) = 2*sqrt(5). - Vaclav Kotesovec, Feb 08 2014 MATHEMATICA Table[Sum[Binomial[n, k]*Binomial[2*(n-k), n]*(-5)^k, {k, 0, Floor[n/2]}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 08 2014 *) CoefficientList[Series[1/Sqrt[1-4x+20x^2], {x, 0, 30}], x] (* Harvey P. Dale, Jul 29 2015 *) CROSSREFS Sequence in context: A057777 A139735 A184952 * A326483 A187468 A238719 Adjacent sequences:  A098334 A098335 A098336 * A098338 A098339 A098340 KEYWORD easy,sign AUTHOR Paul Barry, Sep 03 2004 STATUS approved

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Last modified September 22 06:01 EDT 2021. Contains 347605 sequences. (Running on oeis4.)