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A052183 A second-order recursive sequence. 0
2, 3, 12, 60, 330, 1911, 11424, 69768, 432630, 2713425, 17168580, 109390320, 700939512, 4512458580, 29164264320, 189120846288, 1229917589262, 8018580361365, 52392620853300, 342991368096300, 2249282417749290 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

c(2; n) is equivalent to Eq. (6.22) on p. 129 of the Carlitz reference.

LINKS

Table of n, a(n) for n=0..20.

L. Carlitz, Enumeration of two-line arrays, Fib. Quart., 11 (1973), pp. 113-130.

FORMULA

a(n) = (n+2)*c(2; n), where c(2; n) = C(3n, n)/(2n+1) (A001764).

G.f.: (2-5*g)/((3*g-1)*(g-1)) where g*(1-g)^2 = x. - Mark van Hoeij, Nov 10 2011

conjecture: 2*n*(2*n+1)*a(n) +( -47*n^2+50*n-12)*a(n-1) + 15*(3*n-4)*(3*n-5)*a(n-2) = 0. - R. J. Mathar, Sep 27 2012

MATHEMATICA

Table[(n+2) Binomial[3n, n]/(2n+1), {n, 0, 20}] (* Harvey P. Dale, Mar 23 2013 *)

CROSSREFS

Cf. A001764, A000108.

Sequence in context: A094532 A092980 A191464 * A123899 A188588 A032133

Adjacent sequences:  A052180 A052181 A052182 * A052184 A052185 A052186

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Jan 27 2000

EXTENSIONS

More terms from James A. Sellers, Jan 31 2000

STATUS

approved

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Last modified October 17 08:36 EDT 2019. Contains 328107 sequences. (Running on oeis4.)