This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

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.

Last modified December 10 12:42 EST 2019. Contains 329895 sequences. (Running on oeis4.)