OFFSET
1,2
REFERENCES
Clifford A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Oxford University Press, 2001, p. 325.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
Clifford A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review.
Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).
FORMULA
G.f.: -x*(x^12 +2172*x^11 +247236*x^10+ 6030140*x^9 +49258935*x^8 +163809288*x^7 +242384856*x^6 +163809288*x^5 +49258935*x^4 +6030140*x^3 +247236*x^2 +2172*x +1)/(x-1)^15. - Colin Barker, Jul 09 2012
From Benedict W. J. Irwin, Mar 14 2016: (Start)
G.f.: z*7F6([3,3,3,3,3,3,3], [1,1,1,1,1,1], z).
a(n) = n^7*(1+n)^7/128.
(End)
a(n) = binomial(n+1, 2)^7. - Alejandro Rodriguez, Oct 20 2020
From Amiram Eldar, May 15 2022: (Start)
Sum_{n>=1} 1/a(n) = 219648 - 19712*Pi^2 - 3584*Pi^4/15 - 256*Pi^6/135.
Sum_{n>=1} (-1)^(n+1)/a(n) = 236544*log(2) + 40320*zeta(3) + 6720*zeta(5) + 252*zeta(7) - 219648. (End)
MATHEMATICA
m = 7; Table[ ( (n^m)(n + 1)^m )/(2^m), {n, 1, 20} ]
(Times@@@Partition[Range[20]^7, 2, 1])/2^7 (* Harvey P. Dale, Aug 20 2017 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert G. Wilson v, Mar 06 2001
STATUS
approved