A004256 a(n) = n^2*(n+1)*(n+2)^2/6.

0, 3, 32, 150, 480, 1225, 2688, 5292, 9600, 16335, 26400, 40898, 61152, 88725, 125440, 173400, 235008, 312987, 410400, 530670, 677600, 855393, 1068672, 1322500, 1622400, 1974375, 2384928, 2861082

Offset

0,2

Links

Delbert L. Johnson, Table of n, a(n) for n = 0..19999

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

From Harvey P. Dale, May 26 2015: (Start)

G.f.: (3*x+14*x^2+3*x^3)/(x-1)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6); a(0)=0, a(1)=3, a(2)=32, a(3)=150, a(4)=480, a(5)=1225. (End)

From Amiram Eldar, Nov 02 2021: (Start)

Sum_{n>=1} 1/a(n) = 3/8.

Sum_{n>=1} (-1)^(n+1)/a(n) = 69/8 - 12*log(2). (End)

Mathematica

Table[(n^2 (n+1)(n+2)^2)/6, {n, 0, 40}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 3, 32, 150, 480, 1225}, 40] (* Harvey P. Dale, May 26 2015 *)

Prog

(Magma) [n^2*(n+1)*(n+2)^2/6 : n in [0..50]]; // Wesley Ivan Hurt, Jan 22 2022

Crossrefs

Equals (n+2) * A002417.

Sequence in context: A213845 A221464 A119940 * A183457 A322234 A264574

Adjacent sequences: A004253 A004254 A004255 * A004257 A004258 A004259

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved