0,2

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

Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.

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}.

Cf. A006139, A106259, A106260, A106261.

Sequence in context: A002903 A019482 A090965 this_sequence A085363 A039741 A130185

Adjacent sequences: A106255 A106256 A106257 this_sequence A106259 A106260 A106261

easy,nonn

Paul Barry (pbarry(AT)wit.ie), Apr 28 2005