OFFSET
2,2
COMMENTS
7th binomial transform of (0,0,1,0,0,0,........). Starting at 1, the three-fold convolution of A000420 (powers of 7). - Paul Barry, Mar 08 2003
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 2..400
Index entries for linear recurrences with constant coefficients, signature (21,-147,343).
FORMULA
From Paul Barry, Mar 08 2003: (Start)
G.f.: x^2 / (1-7*x)^3.
a(n) = 21*a(n-1) - 147*a(n-2) + 343*a(n-3), a(0) = a(1) = 0, a(2) = 1. (End)
Numerators of sequence a[3,n] in (a[i,j])^3 where a[i,j] = binomial(i-1, j-1)/2^(i-1) if j<=i, 0 if j>i.
E.g.f.: (x^2/2)*exp(7*x). - G. C. Greubel, May 13 2021
From Amiram Eldar, Jan 06 2022: (Start)
Sum_{n>=2} 1/a(n) = 14 - 84*log(7/6).
Sum_{n>=2} (-1)^n/a(n) = 112*log(8/7) - 14. (End)
MAPLE
seq(binomial(n, 2)*7^(n-2), n=2..30); # Zerinvary Lajos, Jun 12 2008
MATHEMATICA
Table[7^(n-2) Binomial[n, 2], {n, 2, 20}] (* Harvey P. Dale, Sep 25 2011 *)
PROG
(Sage) [7^(n-2)*binomial(n, 2) for n in range(2, 21)] # Zerinvary Lajos, Mar 13 2009
(Magma) [7^(n-2)* Binomial(n, 2): n in [2..20]]; /* Vincenzo Librandi, Oct 12 2011 */
(PARI) a(n)=7^(n-2)*n*(n-1)/2 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Edited by Ralf Stephan, Dec 30 2004
STATUS
approved