A317637 a(n) = n*(n+1)*(n+3).

0, 8, 30, 72, 140, 240, 378, 560, 792, 1080, 1430, 1848, 2340, 2912, 3570, 4320, 5168, 6120, 7182, 8360, 9660, 11088, 12650, 14352, 16200, 18200, 20358, 22680, 25172, 27840, 30690, 33728, 36960, 40392, 44030, 47880, 51948, 56240, 60762, 65520, 70520, 75768, 81270, 87032

Offset

0,2

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = 2*A077414(n+1).

Sum_{n>=1} 1/a(n) = 7/36. - Amiram Eldar, Oct 07 2020

Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/3 - 13/36. - Amiram Eldar, Feb 22 2022

From Elmo R. Oliveira, Sep 08 2025: (Start)

G.f.: 2*x*(4 - x)/(x - 1)^4.

E.g.f.: x*(8 + 7*x + x^2)*exp(x).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)

Mathematica

Table[n*(n + 1)*(n + 3), {n, 0, 43}] (* Giovanni Resta, Aug 10 2018 *)

Crossrefs

Cf. A077414.

Sequence in context: A299279 A184323 A004639 * A131769 A055832 A195753

Adjacent sequences: A317634 A317635 A317636 * A317638 A317639 A317640

Keyword

nonn,easy

Author

Renzo Remotti, Aug 02 2018

Status

approved