A064197 - OEIS

A064197

a(n) = 27*(n-1)*(n-2)*(n-3)*(3*n-8)/2.

0, 0, 324, 2268, 8100, 21060, 45360, 86184, 149688, 243000, 374220, 552420, 787644, 1090908, 1474200, 1950480, 2533680, 3238704, 4081428, 5078700, 6248340, 7609140, 9180864, 10984248, 13041000, 15373800, 18006300, 20963124, 24269868, 27953100, 32040360, 36560160

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

OFFSET

2,3

REFERENCES

Luigi Berzolari, Allgemeine Theorie der Höheren Ebenen Algebraischen Kurven, Encyclopädie der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, Band III_2, Heft 3, Leipzig: B. G. Teubner, 1906, p. 341.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 2..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

G.f.: 324*x^4*(1+2*x)/(1-x)^5. - Colin Barker, Feb 28 2012

From Amiram Eldar, Jun 20 2026: (Start)

Sum_{n>=4} 1/a(n) = 47/270 - Pi/(30*sqrt(3)) - log(3)/10.

Sum_{n>=4} (-1)^n/a(n) = Pi/(15*sqrt(3)) + 8*log(2)/135 - 43/270. (End)

MATHEMATICA

Table[27*(n-1)*(n-2)*(n-3)*(3*n-8)/2, {n, 2, 40}] (* Vincenzo Librandi, Feb 29 2012 *)

PROG

(Magma) [27*(n-1)*(n-2)*(n-3)*(3*n-8)/2: n in [2..30]]; // Vincenzo Librandi, Feb 29 2012