OFFSET
0,4
COMMENTS
Starting at 1, the three-fold convolution of A011557 (powers of 10).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (30,-300,1000).
FORMULA
a(n) = 30*a(n-1) - 300*a(n-2) + 1000*a(n-3), a(0)=a(1)=0, a(2)=1.
a(n) = 10^(n-2)*binomial(n, 2).
G.f.: x^2/(1-10*x)^3.
E.g.f.: (x^2/2)*exp(10*x). - G. C. Greubel, May 13 2021
From Amiram Eldar, Jan 06 2022: (Start)
Sum_{n>=2} 1/a(n) = 20 - 180*log(10/9).
Sum_{n>=2} (-1)^n/a(n) = 220*log(11/10) - 20. (End)
MATHEMATICA
Table[10^(n-2)*Binomial[n, 2], {n, 0, 30}] (* G. C. Greubel, May 13 2021 *)
PROG
(Magma) [10^n* Binomial(n+2, 2): n in [-2..20]]; // Vincenzo Librandi, Oct 16 2011
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 08 2003
STATUS
approved