A119579 a(n) = (n + n^2)*(binomial(2*n, n)).

0, 4, 36, 240, 1400, 7560, 38808, 192192, 926640, 4375800, 20323160, 93117024, 421848336, 1892909200, 8424486000, 37228204800, 163493866080, 714083503320, 3103696272600, 13431200244000, 57895542104400, 248675137991280

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

From Amiram Eldar, Feb 20 2021: (Start)

a(n) = A002378(n)*A000984(n).

Sum_{n>=1} (-1)^(n+1)/a(n) = -1 + 2*sqrt(5)*log(phi) - 4*log(phi)^2, where log(phi) = A002390. (End)

Sum_{n>=1} 1/a(n) = Pi^2/9 - Pi/sqrt(3) + 1. - Amiram Eldar, Jan 24 2022

Maple

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

Mathematica

Table[n*(n + 1)*Binomial[2*n, n], {n, 0, 20}] (* Amiram Eldar, Feb 20 2021 *)

Prog

(PARI) a(n) = (n + n^2)*(binomial(2*n, n)); \\ Michel Marcus, Feb 20 2021

Crossrefs

Cf. A000984, A002378, A002390.

Sequence in context: A003488 A295411 A218516 * A202797 A294832 A075144

Adjacent sequences: A119576 A119577 A119578 * A119580 A119581 A119582

Keyword

easy,nonn

Author

Zerinvary Lajos, May 31 2006

Status

approved