OFFSET
0,2
COMMENTS
Coefficient of x^n in (1 + 3 x + 5 x^2)^n = number of paths from the origin to (n,0) with steps U=(1,1), H=(1,0) and D=(1,-1); U can have 5 colors and H can have 3 colors. - N-E. Fahssi, Jan 28 2008
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Hacène Belbachir, Abdelghani Mehdaoui, László Szalay, Diagonal Sums in the Pascal Pyramid, II: Applications, J. Int. Seq., Vol. 22 (2019), Article 19.3.5.
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(3x)*BesselI(0, 2*sqrt(5)*x)
D-finite with recurrence: n*a(n) = 3*(2*n-1)*a(n-1) + 11*(n-1)*a(n-2). - Vaclav Kotesovec, Oct 15 2012
a(n) ~ sqrt(50+15*sqrt(5))*(3+2*sqrt(5))^n/(10*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 15 2012
MATHEMATICA
Table[SeriesCoefficient[1/Sqrt[1-6*x-11*x^2], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 15 2012 *)
PROG
(PARI) x='x+O('x^66); Vec(1/sqrt(1-6*x-11*x^2)) \\ Joerg Arndt, May 11 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Sep 07 2004
STATUS
approved