A115056 a(n) = n*(n^2-1)*(3*n+2).

0, 0, 0, 48, 264, 840, 2040, 4200, 7728, 13104, 20880, 31680, 46200, 65208, 89544, 120120, 157920, 204000, 259488, 325584, 403560, 494760, 600600, 722568, 862224, 1021200, 1201200, 1404000, 1631448, 1885464, 2168040, 2481240, 2827200

Offset

-1,4

References

George E. Andrews, Number Theory, Dover Publications, New York, 1971, p. 4.

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

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

Formula

From G. C. Greubel, Jul 17 2017: (Start)

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

G.f.: 24*x^2*(x+2)/(1-x)^5.

E.g.f.: (3*x^4 + 20*x^3 + 24*x^2)*exp(x). (End)

From Amiram Eldar, Mar 12 2023: (Start)

Sum_{n>=2} 1/a(n) = 27*log(3)/20 - 3*sqrt(3)*Pi/20 - 16/25.

Sum_{n>=2} (-1)^n/a(n) = 3*sqrt(3)*Pi/10 - 4*log(2)/5 - 53/50. (End)

Mathematica

Table[3*n^4 + 2*n^3 - 3*n^2 - 2*n, {n, -1, 50}] (* G. C. Greubel, Jul 17 2017 *)

Prog

(PARI) g(n) = for(x=0, n, y=x*(x^2-1)*(3*x+2); print1(y", "))
(PARI) my(x='x+O('x^50)); concat([0, 0, 0], Vec(24*x^2*(x+2)/(1-x)^5)) \\ G. C. Greubel, Jul 17 2017

Crossrefs

Sequence in context: A235904 A275406 A205469 * A001337 A259993 A205747

Adjacent sequences: A115053 A115054 A115055 * A115057 A115058 A115059

Keyword

nonn,easy

Author

Cino Hilliard, Feb 28 2006

Status

approved