OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = (1/2) * A000911(n-1).
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
Sum_{n>=1} 1/a(n) = 4 - 2*Pi/sqrt(3). - Amiram Eldar, Oct 22 2020
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[ 3x(1-4x)^(-5/2), {x, 0, n}]; (* Michael Somos, Sep 09 2013 *)
Table[Binomial[2*n, n]*n*(2*n + 1)/2, {n, 0, 22}] (* Amiram Eldar, Oct 22 2020 *)
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 */
(Magma) [Binomial(2*n, n)*n*(2*n+1)/2: n in [0..25]]; // G. C. Greubel, Feb 10 2019
(Sage) [binomial(2*n, n)*n*(2*n+1)/2 for n in (0..25)] # G. C. Greubel, Feb 10 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved