A006631 From generalized Catalan numbers. (Formerly M4539)

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

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

Column 4 of A092276.

Sequence in context: A125345 A111996 A016129 * A205218 A287813 A126503

Adjacent sequences: A006628 A006629 A006630 * A006632 A006633 A006634

Keyword

nonn,easy

Author

Simon Plouffe

Extensions

More terms from Vincenzo Librandi, May 03 2013

Status

approved