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A106258
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Expansion of 1/sqrt(1-8x-8x^2).
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4
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1, 4, 28, 208, 1624, 13024, 106336, 879232, 7338592, 61699456, 521753728, 4433024512, 37812715264, 323603221504, 2777262164992, 23893731463168, 206005885076992, 1779480850438144, 15396895523989504, 133420304211238912
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Central coefficient of (1+4x+6x^2)^n. Fourth binomial transform of 1/sqrt(1-24x^2). In general, 1/sqrt(1-4*r*x-4*r*x^2) has e.g.f. exp(2rx)BesselI(0,2r*sqrt((r+1)/r)x)), a(n)=sum{k=0..n, C(2k,k)C(k,n-k)r^k}, gives the central coefficient of (1+(2r)x+r(r+1)x^2) and is the (2r)-th binomial transform of 1/sqrt(1-8*C(n+1,2)x^2).
Also number of paths from (0,0) to (n,0) using steps U=(1,1), H=(1,0) and D=(1,-1), the H steps can have 4 colors and the U steps can have 6 colors. - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Mar 31 2008
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REFERENCES
| 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(4*x)*BesselI(0, 4*sqrt(3/2)*x); a(n)=sum{k=0..n, C(2k, k)C(k, n-k)2^k}.
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CROSSREFS
| Cf. A006139, A106259, A106260, A106261.
Sequence in context: A019482 A198630 A090965 * A085363 A039741 A130185
Adjacent sequences: A106255 A106256 A106257 * A106259 A106260 A106261
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Apr 28 2005
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