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%I #21 Dec 02 2019 03:13:08
%S 1,2,6,24,116,672,4520,35050,303468,2934652,31145346,361323708,
%T 4535359000,61431851046,890284097146,13784350300996
%N Total number of graceful labelings of connected graphs with n edges.
%C In general, consider a connected graph with E edges and V vertices. The vertices are given labels in the range 0 to E so that the differences between edges' endpoints are {1,...,E}. None of the vertices are isolated; hence each vertex label participates in at least one edge. For this sequence V is unrestricted and E = n.
%H D. E. Knuth, <a href="https://cs.stanford.edu/~knuth/programs/graceful-count.w">Program for counting graceful graph labelings.</a>
%Y Cf. A033472 (V=E+1), A329789 (V=E). A diagonal of the triangle in A329790.
%K nonn,more
%O 1,2
%A _N. J. A. Sloane_, Dec 01 2019, based on email from _Don Knuth_, Dec 01 2019
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