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A059979
Number of 7-dimensional cage assemblies.
2
1, 2187, 279936, 10000000, 170859375, 1801088541, 13492928512, 78364164096, 373669453125, 1522435234375, 5455160701056, 17565568854912, 51676101935731, 140710042265625, 358318080000000, 860542568759296, 1962637152460137, 4275360817613091, 8938717390000000
OFFSET
1,2
REFERENCES
Clifford A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Oxford University Press, 2001, p. 325.
LINKS
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
Sequence in context: A224358 A224017 A016771 * A224315 A224379 A016843
KEYWORD
nonn,easy
AUTHOR
Robert G. Wilson v, Mar 06 2001
STATUS
approved