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A051133 C(2n,n)*n*(2n+1)/2. 6
0, 3, 30, 210, 1260, 6930, 36036, 180180, 875160, 4157010, 19399380, 89237148, 405623400, 1825305300, 8143669800, 36064823400, 158685222960, 694247850450, 3022020054900, 13095420237900, 56517076816200, 243023430309660, 1041528987041400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..22.

FORMULA

a(n) = 1/2 * A000911(n-1).

a(n) = (1/2)*A000984(n+1)*A000217(n). - Zerinvary Lajos, May 05 2007

a(n) = 3*A002802(n-1) - Zerinvary Lajos, Jun 02 2007

(-n+1)*a(n) +2*(2*n+1)*a(n-1)=0. - R. J. Mathar, Feb 05 2013

G.f.: 3*x * (1 - 4*x)^(-5/2). - Michael Somos, Sep 09 2013

EXAMPLE

G.f. = 3*x + 30*x^2 + 210*x^3 + 1260*x^4 + 6930*x^5 + 36036*x^6 + ...

MAPLE

seq(binomial(2*n, n)*binomial(n, (n-2))/2, n=1..23); - Zerinvary Lajos, May 05 2007

MATHEMATICA

a[ n_] := SeriesCoefficient[ 3 x (1 - 4 x)^(-5/2), {x, 0, n}]; (* Michael Somos, Sep 09 2013 *)

PROG

(PARI) {a(n) = if( n<1, 0, (2*n + 1)! / (2 * n! *(n-1)!))}; /* Michael Somos, Sep 09 2013 */

(PARI) {a(n) = 2^(n+2) * polcoeff( pollegendre( n+3), n-1)}; /* Michael Somos, Sep 09 2013 */

CROSSREFS

Sequence in context: A121100 A203366 A130546 * A043030 A178015 A120689

Adjacent sequences:  A051130 A051131 A051132 * A051134 A051135 A051136

KEYWORD

nonn,easy

AUTHOR

Wouter Meeussen

STATUS

approved

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Last modified July 26 02:08 EDT 2017. Contains 289798 sequences.