A085284 a(n) = C(n+3,3)*n^3/4.

0, 1, 20, 135, 560, 1750, 4536, 10290, 21120, 40095, 71500, 121121, 196560, 307580, 466480, 688500, 992256, 1400205, 1939140, 2640715, 3542000, 4686066, 6122600, 7908550, 10108800, 12796875, 16055676, 19978245, 24668560, 30242360, 36828000, 44567336, 53616640

Offset

0,3

Links

Table of n, a(n) for n=0..32.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

a(n) = n^3(n+1)(n+2)(n+3)/4!.

a(n) = C(n+1, n)^2 * C(n+4, n). - Zerinvary Lajos, Jul 29 2005

From Amiram Eldar, Feb 13 2023: (Start)

Sum_{n>=1} 1/a(n) = 449/54 - 11*Pi^2/9 + 4*zeta(3).

Sum_{n>=1} (-1)^(n+1)/a(n) = 224*log(2)/9 - 749/54 - 11*Pi^2/18 + 3*zeta(3). (End)

Mathematica

Table[(Binomial[n+3, 3]*n^3)/4, {n, 0, 30}] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 1, 20, 135, 560, 1750, 4536}, 40] (* Harvey P. Dale, Jan 08 2016 *)

Crossrefs

Cf. A002417.

Sequence in context: A356272 A188145 A168178 * A105573 A144965 A262140

Adjacent sequences: A085281 A085282 A085283 * A085285 A085286 A085287

Keyword

easy,nonn

Author

Paul Barry, Jun 26 2003

Status

approved