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A006630 From generalized Catalan numbers.
(Formerly M4214)
7
1, 6, 33, 182, 1020, 5814, 33649, 197340, 1170585, 7012200, 42364476, 257854776, 1579730984, 9734161206, 60290077905, 375138262520, 2343880406595, 14699630061270, 92502956574105, 583920410197950, 3696470074992240, 23461536762704040, 149270218961671548 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

It appears that this is the self-convolution of A001764 starting 1, 3, 12, ... . - Alon Regev, Aug 07 2015

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

Andrew Howroyd, 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 ( [ 2, 8/3, 7/3 ]; [ 4, 7/2 ]; 27 x / 4 ).

a(n) = C(3n+6, n)*2/(n+2). - Henry Bottomley, Sep 24 2001

G.f.: (1-RootOf(x-t*(1-t)^2,t))^(-6) (algebraic function in Maple notation). - Mark van Hoeij, Nov 08 2011

MATHEMATICA

Table[Binomial[3 n + 6, n] 2 / (n + 2), {n, 0, 25}] (* Vincenzo Librandi, Aug 07 2015 *)

PROG

(MAGMA) [Binomial(3*n+6, n)*2/(n+2): n in [0..25]]; // Vincenzo Librandi, Aug 07 2015

(PARI) a(n) = binomial(3*n+6, n)*2/(n+2); \\ Andrew Howroyd, Nov 06 2017

CROSSREFS

Column 3 of A092276.

Sequence in context: A009162 A012718 A297221 * A180035 A286187 A260774

Adjacent sequences:  A006627 A006628 A006629 * A006631 A006632 A006633

KEYWORD

nonn,easy

AUTHOR

Simon Plouffe

EXTENSIONS

More terms from Christopher Lund (clund(AT)san.rr.com), Apr 16 2002

a(21)-a(22) from Vincenzo Librandi, Aug 07 2015

STATUS

approved

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Last modified February 27 10:25 EST 2021. Contains 341649 sequences. (Running on oeis4.)