OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: x*(9-8*x)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
a(n) = A126890(n,8) for n>7. - Reinhard Zumkeller, Dec 30 2006
If we define f(n,i,a) = Sum_{k=0..n-i} binomial(n,k)*stirling1(n-k,i)* Product_{j=0..k-1} (-a-j), then a(n) = -f(n,n-1,9), for n>=1. - Milan Janjic, Dec 20 2008
a(n) = a(n-1) + n + 8 (with a(0)=0). - Vincenzo Librandi, Aug 07 2010
a(n) = 9*n - floor(n/2) + floor(n^2/2). - Wesley Ivan Hurt, Jun 15 2013
E.g.f.: x*(18 + x)*exp(x)/2. - G. C. Greubel, Jan 19 2020
From Amiram Eldar, Jan 10 2021: (Start)
Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/17 - 1768477/20828808. (End)
MAPLE
seq( n*(n+17)/2, n=0..50); # G. C. Greubel, Jan 19 2020
MATHEMATICA
Table[n(n+17)/2, {n, 0, 50}] (* Harvey P. Dale, Apr 25 2011 *)
PROG
(PARI) a(n)=n*(n+17)/2 \\ Charles R Greathouse IV, Sep 24 2015
(Magma) [n*(n+17)/2: n in [0..50]]; // G. C. Greubel, Jan 19 2020
(Sage) [n*(n+17)/2 for n in (0..50)] # G. C. Greubel, Jan 19 2020
(GAP) List([0..50], n-> n*(n+17)/2 ); # G. C. Greubel, Jan 19 2020
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Jul 07 2000
STATUS
approved