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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 27 11:32 EST 2021. Contains 341656 sequences. (Running on oeis4.)