login
A059980
Number of 8-dimensional cage assemblies.
2
1, 6561, 1679616, 100000000, 2562890625, 37822859361, 377801998336, 2821109907456, 16815125390625, 83733937890625, 360040606269696, 1370114370683136, 4702525276151521, 14774554437890625, 42998169600000000, 117033789351264256, 300283484326400961
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 (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).
FORMULA
G.f.: -x*(x^14 +6544*x^13 +1568215*x^12 +72338144*x^11 +1086859301*x^10 +6727188848*x^9 +19323413187*x^8 +27306899520*x^7 +19323413187*x^6 +6727188848*x^5 +1086859301*x^4 +72338144*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)
MATHEMATICA
m = 8; Table[n^m (n + 1)^m/2^m, {n, 1, 18}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert G. Wilson v, Mar 06 2001
STATUS
approved