login
A006631
From generalized Catalan numbers.
(Formerly M4539)
7
1, 8, 52, 320, 1938, 11704, 70840, 430560, 2629575, 16138848, 99522896, 616480384, 3834669566, 23944995480, 150055305008, 943448717120, 5949850262895, 37628321318280, 238591135349700, 1516500543586560, 9660632784642840, 61670325204822048, 394451619337629792
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
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
Column 4 of A092276.
Sequence in context: A125345 A111996 A016129 * A205218 A287813 A126503
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, May 03 2013
STATUS
approved