OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = (5/2)*(n+2)*(n+3)*(Sum_{j=1..n} Sum_{m=1..j} Sum_{k=1..m} (k^2-1))/(Sum_{j=1..n} Sum_{m=1..j} Sum_{k=1..m} k) = (5/2)*(n+2)*(n+3)*A130857(n)/A000332(n+3).
G.f.: x^2*(30-35*x+11*x^2)/(-1+x)^4. - R. J. Mathar, Nov 14 2007
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=0, a(1)=30, a(2)=85, a(3)=171. - Harvey P. Dale, May 01 2011
MATHEMATICA
Rest[CoefficientList[Series[x^2(30-35x+11x^2)/(-1+x)^4, {x, 0, 30}], x]] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 30, 85, 171}, 30] (* Harvey P. Dale, May 01 2011 *)
PROG
(Magma) [(n-1)*(n+2)*(2*n+11)/2: n in [1..50]]; // Vincenzo Librandi, May 02 2011
(PARI) a(n)=(2*n^3 + 13*n^2 + 7*n - 22)/2 \\ Charles R Greathouse IV, May 02, 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Jul 22 2007
EXTENSIONS
Edited by N. J. A. Sloane, May 01 2011
STATUS
approved