%I #51 May 15 2022 07:32:11
%S 1,2187,279936,10000000,170859375,1801088541,13492928512,78364164096,
%T 373669453125,1522435234375,5455160701056,17565568854912,
%U 51676101935731,140710042265625,358318080000000,860542568759296,1962637152460137,4275360817613091,8938717390000000
%N Number of 7-dimensional cage assemblies.
%D Clifford A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Oxford University Press, 2001, p. 325.
%H T. D. Noe, <a href="/A059979/b059979.txt">Table of n, a(n) for n = 1..1000</a>
%H Clifford A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," <a href="http://www.zentralblatt-math.org/zmath/en/search/?q=an:0983.00008&format=complete">Zentralblatt review</a>.
%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).
%F 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
%F From _Benedict W. J. Irwin_, Mar 14 2016: (Start)
%F G.f.: z*7F6([3,3,3,3,3,3,3], [1,1,1,1,1,1], z).
%F a(n) = n^7*(1+n)^7/128.
%F (End)
%F a(n) = binomial(n+1, 2)^7. - _Alejandro Rodriguez_, Oct 20 2020
%F From _Amiram Eldar_, May 15 2022: (Start)
%F Sum_{n>=1} 1/a(n) = 219648 - 19712*Pi^2 - 3584*Pi^4/15 - 256*Pi^6/135.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 236544*log(2) + 40320*zeta(3) + 6720*zeta(5) + 252*zeta(7) - 219648. (End)
%t m = 7; Table[ ( (n^m)(n + 1)^m )/(2^m), {n, 1, 20} ]
%t (Times@@@Partition[Range[20]^7,2,1])/2^7 (* _Harvey P. Dale_, Aug 20 2017 *)
%Y Cf. A059827, A059860.
%K nonn,easy
%O 1,2
%A _Robert G. Wilson v_, Mar 06 2001