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

1,2

References

Clifford A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Oxford University Press, 2001, p. 325.

Links

Table of n, a(n) for n=1..17.

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

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

Sequence in context: A016760 A203652 A016772 * A038684 A016844 A016892

Adjacent sequences: A059977 A059978 A059979 * A059981 A059982 A059983

Keyword

nonn,easy

Author

Robert G. Wilson v, Mar 06 2001

Status

approved