A059978 a(n) = binomial(n+2,n)^6.

1, 729, 46656, 1000000, 11390625, 85766121, 481890304, 2176782336, 8303765625, 27680640625, 82653950016, 225199600704, 567869252041, 1340095640625, 2985984000000, 6327518887936, 12827693806929, 25002110044521, 47045881000000, 85766121000000, 151939915084881

Offset

0,2

Comments

Number of 6-dimensional cage assemblies.

References

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

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Clifford A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review.

Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Formula

G.f.: (x^10 + 716*x^9 + 37257*x^8 + 450048*x^7 + 1822014*x^6 +2864328*x^5 + 1822014*x^4 + 450048*x^3 + 37257*x^2 + 716*x + 1)/(1-x)^13. - Colin Barker, Jul 09 2012

G.f.: 6F5([3,3,3,3,3,3], [1,1,1,1,1], z). - Benedict W. J. Irwin, Mar 14 2016

a(n) = (1/16)*( 3*S(7,n+1) + 10*S(9,n+1) + 3*S(11,n+1) ), where S(r,n) = Sum_{k = 1..n} k^r. Cf. A059977 and A059980. - Peter Bala, Jul 02 2019

From Amiram Eldar, May 15 2022: (Start)

Sum_{n>=0} 1/a(n) = 2688*Pi^2 + 448*Pi^4/15 + 128*Pi^6/945 - 29568.

Sum_{n>=0} (-1)^n/a(n) = 29568 - 32256*log(2) - 5376*zeta(3) - 720*zeta(5). (End)

Maple

with (combinat):seq(mul(stirling2(n+1, n), k=1..6), n=1..18); # Zerinvary Lajos, Dec 14 2007

Mathematica

m = 6; Table[n^m (n + 1)^m/2^m, {n, 1, 24}]

Crossrefs

Cf. A059827, A059860, A000217, A059977, A059980, A091043.

Sequence in context: A224357 A016770 A224016 * A223208 A005608 A233025

Adjacent sequences: A059975 A059976 A059977 * A059979 A059980 A059981

Keyword

nonn,easy

Author

Robert G. Wilson v, Mar 06 2001

Extensions

Better definition from Zerinvary Lajos, May 23 2006

Status

approved