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A097321

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

24, 210, 720, 1716, 3360, 5814, 9240, 13800, 19656, 26970, 35904, 46620, 59280, 74046, 91080, 110544, 132600, 157410, 185136, 215940, 249984, 287430, 328440, 373176, 421800, 474474, 531360, 592620, 658416, 728910, 804264, 884640, 970200, 1061106, 1157520

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

S. Ramanujan, Notebook entry.

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

FORMULA

G.f.: 6x * (4x^2 + 19x + 4) / (1-x)^4.

Sum_{n>=1} 1/a(n) = (log(3) - 1)/2. - Amiram Eldar, Jul 04 2020

Sum_{n>=1} (-1)^(n+1)/a(n) = 1/2 - 2*log(2)/3. - Amiram Eldar, May 15 2022

E.g.f.: 3*exp(x)*x*(8 + 27*x + 9*x^2). - Stefano Spezia, Feb 20 2025