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A098264
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G.f.: 1/(1-2x-19x^2)^(1/2).
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5
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1, 1, 11, 31, 211, 851, 4901, 22961, 124531, 623011, 3313201, 17086301, 90453661, 473616781, 2509264811, 13250049551, 70368250451, 373539254611, 1989045489281, 10597110956861, 56566637447401, 302196871378601
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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. - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Mar 31 2008
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LINKS
| Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.
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FORMULA
| E.g.f. : exp(x)BesselI(0, 2sqrt(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
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CROSSREFS
| Cf. A084601, A084603, A084605.
Sequence in context: A002535 A128337 A093382 * A023279 A068715 A093881
Adjacent sequences: A098261 A098262 A098263 * A098265 A098266 A098267
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Aug 31 2004
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