OFFSET
1,2
COMMENTS
This is the case k = n of b(n,k) = n*(n+1)*(n+2)*(n+3)*(n+4)*(k*(n-1)+6)/120, where b(n,k) is the n-th hypersolid number in 6 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:0805.4070 [math.GM], 2008.
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
FORMULA
G.f.: x*(1 + 6*x^2)/(1 - x)^8.
MATHEMATICA
Table[n (1 + n) (2 + n) (3 + n) (4 + n) (6 - n + n^2)/720, {n, 40}]
Table[Times@@(n+Range[0, 4])(n^2-n+6)/720, {n, 40}] (* or *) LinearRecurrence[ {8, -28, 56, -70, 56, -28, 8, -1}, {1, 8, 42, 168, 546, 1512, 3696, 8184}, 40] (* Harvey P. Dale, Sep 25 2019 *)
PROG
(PARI) vector(40, n, n*(n+1)*(n+2)*(n+3)*(n+4)*(n^2-n+6)/720) \\ Bruno Berselli, Apr 15 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Luciano Ancora, Apr 14 2015
STATUS
approved