A256860 a(n) = n*(n + 1)*(n + 2)*(n + 3)*(n^2 - n + 5)/120.

1, 7, 33, 119, 350, 882, 1974, 4026, 7623, 13585, 23023, 37401, 58604, 89012, 131580, 189924, 268413, 372267, 507661, 681835, 903210, 1181510, 1527890, 1955070, 2477475, 3111381, 3875067, 4788973, 5875864, 7161000, 8672312, 10440584, 12499641, 14886543

Offset: 1

Author

Luciano Ancora, Apr 14 2015

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000579.

Cf. similar sequences listed in A256859.

Programs

Mathematica

Table[n (n + 1) (n + 2) (n + 3) (n^2 - n + 5)/120, {n, 40}]

PARI

vector(40, n, n*(n+1)*(n+2)*(n+3)*(n^2-n+5)/120) \\ Bruno Berselli, Apr 15 2015

Formula

G.f.: x*(1 + 5*x^2)/(1 - x)^7.

a(n) = 5*A000579(n+3) + A000579(n+5). [Bruno Berselli, Apr 15 2015]