OFFSET
1,2
COMMENTS
This is the case k = n of b(n,k) = n*(n+1)*(n+2)*(n+3)*(k*(n-1)+5)/120, where b(n,k) is the n-th hypersolid number in 5 dimensions generated from an arithmetical progression with the first term 1 and common difference k (see Sardelis et al. paper).
LINKS
D. A. Sardelis and T. M. Valahas, On Multidimensional Pythagorean Numbers, arXiv:0805.4070v1 [math.GM], 2008.
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
G.f.: x*(1 + 5*x^2)/(1 - x)^7.
MATHEMATICA
Table[n (n + 1) (n + 2) (n + 3) (n^2 - n + 5)/120, {n, 40}]
PROG
(PARI) vector(40, n, n*(n+1)*(n+2)*(n+3)*(n^2-n+5)/120) \\ Bruno Berselli, Apr 15 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Luciano Ancora, Apr 14 2015
STATUS
approved