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 A098264 G.f.: 1/(1-2x-19x^2)^(1/2). 7
 1, 1, 11, 31, 211, 851, 4901, 22961, 124531, 623011, 3313201, 17086301, 90453661, 473616781, 2509264811, 13250049551, 70368250451, 373539254611, 1989045489281, 10597110956861, 56566637447401, 302196871378601, 1616570627763311, 8654955238504531, 46384344189261661 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Central coefficient of (1+x+5x^2)^n. Also number of paths from (0,0) to (n,0) using steps U=(1,1), H=(1,0) and D=(1,-1), the U steps can have five colors. - N-E. Fahssi, Mar 31 2008 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..300 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(x)*BesselI(0, 2*sqrt(5)x). a(n) = sum{k=0..floor(n/2), binomial(n, k)*binomial(n-k, k)*5^k}. a(n) = sum{k=0..floor(n/2), binomial(n, 2k)*binomial(2k, k)*5^k}. n*a(n) +(1-2*n)*a(n-1) +19*(1-n)*a(n-2)=0. - R. J. Mathar, Nov 14 2011 a(n) ~ sqrt(50+5*sqrt(5))*(1+2*sqrt(5))^n/(10*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 14 2012 MATHEMATICA Table[SeriesCoefficient[1/Sqrt[1-2*x-19*x^2], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 14 2012 *) PROG (PARI) x='x+O('x^66); Vec(1/(1-2*x-19*x^2)^(1/2)) \\ Joerg Arndt, May 11 2013 CROSSREFS Cf. A084601, A084603, A084605. Sequence in context: A002535 A128337 A093382 * A023279 A068715 A093881 Adjacent sequences:  A098261 A098262 A098263 * A098265 A098266 A098267 KEYWORD easy,nonn AUTHOR Paul Barry, Aug 31 2004 STATUS approved

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Last modified June 16 19:49 EDT 2021. Contains 345068 sequences. (Running on oeis4.)