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

1,2

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

Cf. A059827, A059860.

Sequence in context: A224358 A224017 A016771 * A224315 A224379 A016843

Adjacent sequences: A059976 A059977 A059978 * A059980 A059981 A059982

Keyword

nonn,easy

Author

Robert G. Wilson v, Mar 06 2001

Status

approved