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Number of balanced symmetric graphs.
(Formerly M1017)
1

%I M1017 #21 Oct 28 2023 09:33:16

%S 1,2,4,6,10,22,38,102,182,574,1070,3798,7286,28894,57374,248502,

%T 506678,2384254,5007230,25247958,54311126,292500574,645652574,

%U 3680048502,8301671798,49967727934,115334270270,728281984278,1714641313046,11341092707614

%N Number of balanced symmetric graphs.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H David A. Sheppard, <a href="http://dx.doi.org/10.1016/0012-365X(76)90051-0">The factorial representation of balanced labelled graphs</a>, Discrete Math. 15 (1976), no. 4, 379-388.

%F Let S(n,j) = j! * j^floor((n-2)/2). If n is even, then a(n) = 2 * Sum_{j=1..n/2} S(n,j). If n is odd, and (n-1)/2 is odd, then a(n) = ((n+1)/2)! + 2 * Sum_{j=1,3,5,...,(n-1)/2} S(n, j). Otherwise, n is odd, and (n-1)/2 is even, then a(n) = ((n+1)/2)! + ((n-1)/2)! + 2 * Sum_{j=1,3,5,...,(n-1)/2-1} S(n, j) [From Sheppard paper]. - _Sean A. Irvine_, Apr 18 2016

%K nonn

%O 1,2

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, Apr 18 2016