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A033678
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Number of labeled Eulerian graphs with n nodes.
(Formerly M3146)
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3
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1, 0, 1, 3, 38, 720, 26614, 1858122, 250586792, 66121926720, 34442540326456, 35611003057733928, 73321307277341501168, 301201690357187097528960, 2471354321681605983102370864, 40525241311304939167532163726672
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OFFSET
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1,4
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REFERENCES
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F. Harary and E. Palmer, Graphical Enumeration, (1973), p. 12, Eq. (1.4.6).
E. M. Palmer in L. W. Beineke and R. J. Wilson, Selected Topics in Graph Theory, Academic Press, NY, 1978, p. 385ff.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..50
Huantian Cao, AutoGF: An Automated System to Calculate Coefficients of Generating Functions.
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MAPLE
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A033678 := proc(n) option remember; local k; if n=1 then 1 else 2^binomial(n-1, 2)-(1/n)*add(k*binomial(n, k)*2^binomial(n-k-1, 2)*A033678(k), k=1..n-1); fi; end;
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MATHEMATICA
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Normal[ Series[ Log[ 1 + Sum[ 2^( (p-1)(p-2)/2 )x^p/(p!), {p, 1, n} ] ], {x, 0, n} ] ] (* truncated exponential generating function *)
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CROSSREFS
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Sequence in context: A156071 A199025 A005780 * A072331 A109518 A158119
Adjacent sequences: A033675 A033676 A033677 * A033679 A033680 A033681
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KEYWORD
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easy,nonn,nice
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AUTHOR
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N. J. A. Sloane, Geoffrey Mess (mess(AT)math.ucla.edu)
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STATUS
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approved
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