OFFSET
4,1
LINKS
T. D. Noe, Table of n, a(n) for n = 4..1000
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
FORMULA
a(n)= A090447(n, 4)= (n^4*(n-1)^3*(n-2)^2*(n-3)^1)/(1!*2!*3!*4!), n>=4.
G.f.: -x^4*(x^6+109*x^5+1435*x^4+4735*x^3+4780*x^2+1444*x+96)/(x-1)^11. - Colin Barker, Jan 21 2013
From Amiram Eldar, Sep 08 2022: (Start)
Sum_{n>=4} 1/a(n) = 700*Pi^2/9 + 4*Pi^4/15 - 40*zeta(3) - 20129/27.
Sum_{n>=4} (-1)^n/a(n) = 30311/27 - 26*Pi^2/9 - 7*Pi^4/30 - 11008*log(2)/9 - 186*zeta(3). (End)
MATHEMATICA
LinearRecurrence[{11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1}, {96, 2500, 27000, 180075, 878080, 3429216, 11340000, 32942250, 86248800, 207352860, 464199736}, 40] (* Harvey P. Dale, Apr 10 2018 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Dec 23 2003
STATUS
approved