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
KEYWORD
nonn,easy
AUTHOR
Cino Hilliard, Feb 28 2006
STATUS
approved