OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
S. Klavzar, A. Rajapakse and I. Gutman, The Szeged and the Wiener index of graphs, Appl. Math. Lett., Vol. 9, No. 5 (1996), pp. 45-49.
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
a(n) = (1/3)*n^4*(n^2 - 1).
G.f.: 8*x^2*(1+x)*(2+11*x+2*x^2)/(1-x)^7.
a(n) = A245826(n,n).
a(n) = 4 * A208954(n).
From Amiram Eldar, Jan 09 2022: (Start)
Sum_{n>=2} 1/a(n) = 33/4 - Pi^2/2 - Pi^4/30.
Sum_{n>=2} (-1)^n/a(n) = 7*Pi^4/240 + Pi^2/4 - 21/4. (End)
MAPLE
a := proc (n) options operator, arrow: (1/3)*n^4*(n^2-1) end proc: seq(a(n), n = 1 .. 40);
MATHEMATICA
CoefficientList[Series[8 x (1 + x) (2 + 11 x + 2 x^2)/(1 - x)^7, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 07 2014 *)
Table[(n^4 (n^2-1))/3, {n, 40}] (* Harvey P. Dale, Mar 25 2021 *)
PROG
(Magma) [n^4*(n^2-1)/3: n in [1..40]]; // Vincenzo Librandi, Aug 07 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Aug 06 2014
STATUS
approved