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

%I A059978 #45 May 15 2022 07:31:21
%S A059978 1,729,46656,1000000,11390625,85766121,481890304,2176782336,
%T A059978 8303765625,27680640625,82653950016,225199600704,567869252041,
%U A059978 1340095640625,2985984000000,6327518887936,12827693806929,25002110044521,47045881000000,85766121000000,151939915084881
%N A059978 a(n) = binomial(n+2,n)^6.
%C A059978 Number of 6-dimensional cage assemblies.
%D A059978 Clifford A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Oxford University Press, 2001, p. 325.
%H A059978 T. D. Noe, <a href="/A059978/b059978.txt">Table of n, a(n) for n = 0..1000</a>
%H A059978 Clifford A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," <a href="http://www.zentralblatt-math.org/zmath/en/search/?q=an:0983.00008&amp;format=complete">Zentralblatt review</a>.
%H A059978 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F A059978 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
%F A059978 G.f.: 6F5([3,3,3,3,3,3], [1,1,1,1,1], z). - _Benedict W. J. Irwin_, Mar 14 2016
%F A059978 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
%F A059978 From _Amiram Eldar_, May 15 2022: (Start)
%F A059978 Sum_{n>=0} 1/a(n) = 2688*Pi^2 + 448*Pi^4/15 + 128*Pi^6/945 - 29568.
%F A059978 Sum_{n>=0} (-1)^n/a(n) = 29568 - 32256*log(2) - 5376*zeta(3) - 720*zeta(5). (End)
%p A059978 with (combinat):seq(mul(stirling2(n+1,n),k=1..6),n=1..18); # _Zerinvary Lajos_, Dec 14 2007
%t A059978 m = 6; Table[n^m (n + 1)^m/2^m, {n, 1, 24}]
%Y A059978 Cf. A059827, A059860, A000217, A059977, A059980, A091043.
%K A059978 nonn,easy
%O A059978 0,2
%A A059978 _Robert G. Wilson v_, Mar 06 2001
%E A059978 Better definition from _Zerinvary Lajos_, May 23 2006