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 A098456 Expansion of 1/sqrt(1-4x-64x^2). 1
 1, 2, 38, 212, 2566, 20092, 210524, 1884136, 18854854, 178415852, 1764019828, 17115907096, 169100140444, 1661540282456, 16458178007288, 162887627833552, 1618680238292294, 16095872154638156, 160435286115927044 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Define Q(n,x)=sum{k=0..floor(n/2), binomial(n,k)binomial(2(n-k),n)x^(n-2k)}. Then a(n)=4^n*Q(n,1/4). Central coefficients of (1+2x+17x^2)^n. 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. FORMULA E.g.f.: exp(2x)*BesselI(0, 2*sqrt(17)*x). a(n) = Sum_{k=0..floor(n/2)} binomial(n, k)*binomial(2(n-k), n)*16^k. D-finite with recurrence: n*a(n) +2*(1-2*n)*a(n-1) +64*(1-n)*a(n-2)=0. - R. J. Mathar, Sep 26 2012 a(n) ~ sqrt(578+34*sqrt(17))*(2+2*sqrt(17))^n/(34*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 15 2012 MATHEMATICA CoefficientList[Series[1/Sqrt[1-4x-64x^2], {x, 0, 30}], x] (* Harvey P. Dale, Dec 27 2011 *) PROG (PARI) x='x+O('x^66); Vec(1/sqrt(1-4*x-64*x^2)) \\ Joerg Arndt, May 11 2013 CROSSREFS Cf. A084770, A098455. Sequence in context: A337773 A364714 A105645 * A214909 A226402 A217214 Adjacent sequences: A098453 A098454 A098455 * A098457 A098458 A098459 KEYWORD easy,nonn AUTHOR Paul Barry, Sep 08 2004 STATUS approved

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Last modified September 10 03:08 EDT 2024. Contains 375770 sequences. (Running on oeis4.)