OFFSET
0,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
a(n) = binomial(n+4, 4)*(15+4*n)/5.
G.f.: (3+x)/(1-x)^6.
a(-n-4) = -A034263(n). - Bruno Berselli, Aug 23 2011
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - Wesley Ivan Hurt, Apr 16 2023
From Amiram Eldar, Oct 14 2025: (Start)
Sum_{n>=0} 1/a(n) = 20 * (4928*Pi + 5135 - 29568*log(2)) / 5929.
Sum_{n>=0} (-1)^n/a(n) = 40 * (2464*sqrt(2)*Pi - 5829 - 308*(8*sqrt(2)-5)*log(2) + 4928*sqrt(2)*log(2-sqrt(2))) / 5929. (End)
MATHEMATICA
a[n_]:=Binomial[n+4, 4]*(15+4*n)/5; Table[a[n], {n, 0, 5!}] (* Vladimir Joseph Stephan Orlovsky, May 30 2010 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Feb 02 2001
EXTENSIONS
More terms from Vladimir Joseph Stephan Orlovsky, May 30 2010
STATUS
approved