OFFSET
0,2
REFERENCES
H. M. Finucan, Some decompositions of generalized Catalan numbers, pp. 275-293 of Combinatorial Mathematics IX. Proc. Ninth Australian Conference (Brisbane, August 1981). Ed. E. J. Billington, S. Oates-Williams and A. P. Street. Lecture Notes Math., 952. Springer-Verlag, 1982.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Emanuele Munarini, Shifting Property for Riordan, Sheffer and Connection Constants Matrices, Journal of Integer Sequences, Vol. 20 (2017), Article 17.8.2.
FORMULA
G.f.: 3_F_2 ( [ 3, 8/3, 10/3 ]; [ 5, 9/2 ]; 27 x / 4 ).
Recurrence: 2*(n+4)*(2*n+7)*a(n) = (5*n+13)*(11*n+29)*a(n-1) - 7*(31*n^2+87*n+62)*a(n-2) + 21*(3*n-1)*(3*n+1)*a(n-3). - Vaclav Kotesovec, Oct 07 2012
a(n) ~ 3^(3n+15/2)/(2^(2n+6)*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 07 2012
a(n) = 8*binomial(3*n + 8, n)/(3*n + 8). - Andrew Howroyd, Nov 06 2017
MATHEMATICA
Table[SeriesCoefficient[HypergeometricPFQ[{3, 8/3, 10/3}, {5, 9/2}, 27*x/4], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 07 2012 *)
PROG
(PARI) a(n) = 8*binomial(3*n + 8, n)/(3*n + 8);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, May 03 2013
STATUS
approved