A059979 Number of 7-dimensional cage assemblies.

1, 2187, 279936, 10000000, 170859375, 1801088541, 13492928512, 78364164096, 373669453125, 1522435234375, 5455160701056, 17565568854912, 51676101935731, 140710042265625, 358318080000000, 860542568759296, 1962637152460137, 4275360817613091, 8938717390000000

Offset: 1

Author

Robert G. Wilson v, Mar 06 2001

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A059827, A059860.

Programs

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 *)

Formula

G.f.: -x*(x^12 +2172*x^11 +247236*x^10+ 6030140*x^9 [phone]*x^8 [phone]*x^7 [phone]*x^6 [phone]*x^5 [phone]*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)