OFFSET
1,2
COMMENTS
This sequence is related to A001296 by a(n) = n*A001296(n) - Sum_{i=0..n-1} A001296(i) with n>0. - Bruno Berselli, Jan 21 2013
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
a(n) = n*(n+1)*(n+2)*(12*n^2+9*n-1)/120.
G.f.: x*(1+7*x+4*x^2) / (x-1)^6. - R. J. Mathar, Sep 15 2012
a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - Wesley Ivan Hurt, Nov 19 2014
a(n) = Sum_{i=1..n} ( i*Sum_{k=1..i} i*k ). - Wesley Ivan Hurt, Nov 19 2014
MAPLE
A086689:=n->n*(n+1)*(n+2)*(12*n^2+9*n-1)/120: seq(A086689(n), n=1..40); # Wesley Ivan Hurt, Nov 19 2014
MATHEMATICA
Table[n (n + 1) (n + 2) (12 n^2 + 9 n - 1)/120, {n, 40}] (* Wesley Ivan Hurt, Nov 19 2014 *)
CoefficientList[Series[(1 + 7 x + 4 x^2) / (x - 1)^6, {x, 0, 50}], x] (° Vincenzo Librandi, Nov 20 2014 °)
PROG
(PARI) t(n)=n*(n+1)/2 for(i=1, 30, print1(", "sum(j=1, i, j^2*t(i))))
(Magma) [n*(n+1)*(n+2)*(12*n^2+9*n-1)/120 : n in [1..40]]; // Wesley Ivan Hurt, Nov 19 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jon Perry, Jul 28 2003
STATUS
approved