OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
a(0)=0, a(1)=108, a(2)=1152, a(3)=6000, a(4)=21600, a(5)=61740, a(6)=150528, a(n)=7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+ a(n-7). - Harvey P. Dale, Mar 29 2012
G.f.: -((12*(x^4+17*x^3+33*x^2+9 x))/(x-1)^7). - Harvey P. Dale, Mar 29 2012
From Amiram Eldar, Apr 03 2021: (Start)
Sum_{n>=1} 1/a(n) = 69/16 - 3*Pi^2/8 - zeta(3)/2.
Sum_{n>=1} (-1)^(n+1)/a(n) = 55/16 - Pi^2/48 - 4*log(2) - 3*zeta(3)/8. (End)
EXAMPLE
a(1) = 1 * (1+1)^2 * (1+2)^3 = 108.
MATHEMATICA
Table[n*(n + 1)^2*(n + 2)^3, {n, 0, 25}] (* Stefan Steinerberger, Feb 26 2006 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 108, 1152, 6000, 21600, 61740, 150528}, 30] (* Harvey P. Dale, Mar 29 2012 *)
PROG
(Maxima) A101213(n):=n*(n+1)^2*(n+2)^3$ makelist(A101213(n), n, 0, 20); /* Martin Ettl, Dec 15 2012 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Parthasarathy Nambi, Dec 13 2004
EXTENSIONS
More terms from Stefan Steinerberger, Feb 26 2006
STATUS
approved