OFFSET
0,2
FORMULA
a(n) = n * (n+1) * (2*n+1) * (17*n^4+34*n^3+28*n^2+11*n+15) / 105.
From Chai Wah Wu, Jun 09 2020: (Start)
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n > 7.
G.f.: 6*x*(x + 1)*(x^4 + 24*x^3 + 86*x^2 + 24*x + 1)/(x - 1)^8. (End)
MATHEMATICA
a[n_] := Coefficient[Expand[Sum[k * (x^k + x^(-k)), {k, 0, n}]^4], x, 0]; Array[a, 30, 0] (* Amiram Eldar, Dec 16 2018 *)
PROG
(PARI) {a(n) = polcoeff((sum(k=0, n, k*(x^k+x^(-k))))^4, 0, x)}
(PARI) {a(n) = n*(n+1)*(2*n+1)*(17*n^4+34*n^3+28*n^2+11*n+15)/105}
(GAP) List([0..30], n->n*(n+1)*(2*n+1)*(17*n^4+34*n^3+28*n^2+11*n+15)/105); # Muniru A Asiru, Dec 16 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 16 2018
STATUS
approved