A092467 a(n) = Sum_{i+j+k=n, 0<=i,j,k<=n} (n+2k)!/(i! * j! * (3*k)!).

1, 3, 13, 63, 309, 1511, 7373, 35951, 175269, 854455, 4165565, 20307647, 99002389, 482649479, 2352978861, 11471077391, 55922991237, 272631840855, 1329115610269, 6479611111519, 31588945184245, 154000207833639

Offset: 0

Author

Benoit Cloitre, Mar 25 2004

Keywords

• nonn

Comments

In general, Sum_{k=0..n} C(n+2k,3k)*r^k has g.f. (1-r*x)^2/(1-(3r+1)*x+3r^2*x^2-r^3*x^3). - Paul Barry, Aug 23 2007

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (7, -12, 8).

Crossrefs

Cf. A007583.

Formula

G.f.: (1-4x+4x^2)/(1-7x+12x^2-8x^3). - Ralf Stephan, Dec 02 2004

a(n) = Sum_{k=0..n} C(n+2k,3k)*2^(n-k). - Paul Barry, Aug 23 2007