A059980 Number of 8-dimensional cage assemblies.

1, 6561, 1679616, 100000000, 2562890625, 37822859361, 377801998336, 2821109907456, 16815125390625, 83733937890625, 360040606269696, 1370114370683136, 4702525276151521, 14774554437890625, 42998169600000000, 117033789351264256, 300283484326400961

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

• Clifford A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review.
• Index entries for linear recurrences with constant coefficients, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).

Crossrefs

Cf. A059827, A059860, A059977, A059978, A091043.

Programs

Mathematica

m = 8; Table[n^m (n + 1)^m/2^m, {n, 1, 18}]

Formula

G.f.: -x*(x^14 +6544*x^13 +1568215*x^12 [phone]*x^11 [phone]*x^10 [phone]*x^9 [phone]*x^8 [phone]*x^7 [phone]*x^6 [phone]*x^5 [phone]*x^4 [phone]*x^3 +1568215*x^2 +6544*x +1)/(x-1)^17. - Colin Barker, Jul 09 2012

From Peter Bala, Jul 02 2019 (Start)

a(n) = (n*(n + 1)/2)^8.

a(n) = (1/16)*( S(9,n) + 7*S(11,n) + 7*S(13,n) + S(15,n) ), where S(r,n) = Sum_{k = 1..n} k^r. Cf. A059977 and A059978. (End)

From Amiram Eldar, May 15 2022: (Start)

Sum_{n>=1} 1/a(n) = 146432*Pi^2 + 5632*Pi^4/3 + 2048*Pi^6/105 + 256*Pi^8/4725 - 1647360.

Sum_{n>=1} (-1)^(n+1)/a(n) = 1647360 - 1757184*log(2) - 304128*zeta(3) - 57600*zeta(5) - 4032*zeta(7). (End)