A059860 a(n) = binomial(n+1, 2)^5.

1, 243, 7776, 100000, 759375, 4084101, 17210368, 60466176, 184528125, 503284375, 1252332576, 2887174368, 6240321451, 12762815625, 24883200000, 46525874176, 83841135993, 146211169851, 247609900000, 408410100000, 657748550151, 1036579476493, 1601568101376

Offset

1,2

Comments

Number of 5-dimensional cage assemblies.

See Chap. 61, "Hyperspace Prisons", of C. Pickover's book "Wonders of Numbers" for full explanation of "cage numbers."

References

Clifford A. Pickover, Wonders of Numbers, Oxford University Press, 2001, p. 325.

Links

Harry J. Smith, 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 (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Formula

L(n) = ((n^m)(n + 1)^m)/(2^m) where m is the dimension.

G.f.: x * (x^8 +232*x^7 +5158*x^6+ 27664*x^5 +47290*x^4 +27664*x^3 +5158*x^2 +232*x +1) / (1-x)^11. - Colin Barker, Jun 28 2012

From Amiram Eldar, May 15 2022: (Start)

Sum_{n>=1} 1/a(n) = 4032 - 1120*Pi^2/3 - 32*Pi^4/9.

Sum_{n>=1} (-1)^(n+1)/a(n) = 4480*log(2) + 720*zeta(3) + 60*zeta(5) - 4032. (End)

Maple

for n from 1 to 100 do printf(`%d, `, ((n^5)*(n + 1)^5)/(2^5) ) od:
with (combinat):seq(mul(stirling2(n+1, n), k=1..5), n=1..21); # Zerinvary Lajos, Dec 14 2007

Mathematica

m = 5; Table[ ( (n^m)(n + 1)^m )/(2^m), {n, 1, 26} ]
Table[Binomial[n+1, 2]^5, {n, 20}] (* Harvey P. Dale, May 04 2018 *)

Prog

(PARI) { for (n=1, 1000, write("b059860.txt", n, " ", (n*(n + 1)/2)^5); ) } \\ Harry J. Smith, Jun 29 2009

Crossrefs

Cf. A059827.

Sequence in context: A224356 A016769 A224015 * A268975 A223207 A224313

Adjacent sequences: A059857 A059858 A059859 * A059861 A059862 A059863

Keyword

easy,nonn

Author

Jason Earls, Feb 28 2001

Extensions

More terms from James A. Sellers, Feb 28 2001

Better definition from Zerinvary Lajos, May 23 2006

Corrected the definition from binomial(n+2,2)^5 to binomial(n+1,2)^5. - Harry J. Smith, Jun 29 2009

Status

approved