OFFSET
0,2
COMMENTS
Number of ascending runs in {1,...,n}^7.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
From Amiram Eldar, Nov 17 2025: (Start)
Sum_{n>=1} 1/a(n) = Pi^6/2835 + 8*Pi^4/1215 + 128*Pi^2/729 - 512*Pi/729 - 64*zeta(3)/81 - 4*zeta(5)/9 + 1024*log(2)/243 - 4096/2187.
Sum_{n>=1} (-1)^(n+1)/a(n) = 31*Pi^6/90720 + 7*Pi^4/1215 + 64*Pi^2/729 - 512*sqrt(2)*Pi/729 - 16*zeta(3)/27 - 5*zeta(5)/12 - (512/729)*(2*log(2) - 2*sqrt(2)*arcsinh(1)) + 4096/2187. (End)
FORMULA
G.f.: (x^6+312*x^5+4029*x^4+9664*x^3+5499*x^2+648*x+7)*x/(x-1)^8.
MAPLE
a:= n-> n^6*(4*n+3):
seq(a(n), n=0..40);
MATHEMATICA
Table[n^6 (4n+3), {n, 0, 40}] (* Harvey P. Dale, Oct 10 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Sep 15 2013
STATUS
approved
