A119581 a(n) = (2*n+n^2)*(binomial(2*n,n))/2.

0, 3, 24, 150, 840, 4410, 22176, 108108, 514800, 2406690, 11085360, 50438388, 227149104, 1014058500, 4493059200, 19777483800, 86555576160, 376877404530, 1633524354000, 7051380128100, 30326236340400, 129989276677260, 555482126422080, 2367111334185000, 10061252349127200

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

From Amiram Eldar, Sep 04 2022: (Start)

a(n) = A005563(n)*A000984(n)/2.

Sum_{n>=1} 1/a(n) = 13/2 - 7*Pi/sqrt(3) + 2*Pi^2/3.

Sum_{n>=1} (-1)^(n+1)/a(n) = 11/2 - 10*sqrt(5)*log(phi) + 24*log(phi)^2, where phi is the golden ratio (A001622). (End)

Maple

[seq ((2*n+n^2)*(binomial(2*n, n))/2, n=0..29)];

Mathematica

Table[(2n+n^2)Binomial[2*n, n]/2, {n, 0, 25}]  (* Harvey P. Dale, Feb 20 2011 *)

Crossrefs

Cf. A000984, A001622, A005563.

Sequence in context: A125651 A043017 A003443 * A367119 A240916 A006292

Adjacent sequences: A119578 A119579 A119580 * A119582 A119583 A119584

Keyword

easy,nonn

Author

Zerinvary Lajos, May 31 2006

Status

approved