|
%I M3725 #46 Nov 25 2017 09:27:44
%S 1,1,4,384,42467328,20776019874734407680,
%T 1657509127047778993870601546036901052416000000,
%U 153850844349814660487100539994381178281567942393055761257560677644718869248475136000000000000000000000
%N Complexity of tensor sum of n graphs; or spanning trees on n-cube.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.6.10.
%H Alois P. Heinz, <a href="/A006237/b006237.txt">Table of n, a(n) for n = 0..10</a>
%H Aaron R. Bagheri, <a href="http://scholarship.claremont.edu/hmc_theses/102">Classifying the Jacobian Groups of Adinkras</a>, (2017), HMC Senior Theses.
%H Frank Harary, John P. Hayes, and Horng-Jyh Wu, <a href="http://dx.doi.org/10.1016/0898-1221(88)90213-1">A survey of the theory of hypercube graphs</a>, Comput. Math. Appl., 15(4) (1988), 277-289.
%H D. E. Knuth, <a href="/A006235/a006235.pdf">Letter to N. J. A. Sloane, Oct. 1994</a>
%H Germain Kreweras, <a href="http://dx.doi.org/10.1016/0095-8956(78)90021-7">Complexité et circuits Eulériens dans les sommes tensorielles de graphes</a>, J. Combin. Theory, B 24 (1978), 202-212. See p. 210, Parag. 4.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HypercubeGraph.html">Hypercube Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SpanningTree.html">Spanning Tree</a>
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F a(n) = 2^(2^n-1-n)*1^binomial(n, 1)*2^binomial(n, 2)*...*n^binomial(n, n).
%t Table[2^(2^n - 1 - n) Product[k^Binomial[n, k], {k, n}], {n, 0, 10}]
%o (PARI) a(n)=2^(2^n-n-1)*prod(k=1,n,k^binomial(n,k))
%Y Cf. A006235.
%K nonn,easy,nice
%O 0,3
%A _N. J. A. Sloane_, _Don Knuth_
%E Description expanded July 1995
| 