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Search: id:A033678
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| A033678 |
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Number of labeled Eulerian graphs with n nodes.
(Formerly M3146)
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+0
3
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| 1, 0, 1, 3, 38, 720, 26614, 1858122, 250586792, 66121926720, 34442540326456, 35611003057733928, 73321307277341501168, 301201690357187097528960, 2471354321681605983102370864, 40525241311304939167532163726672
(list; graph; listen)
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OFFSET
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1,4
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
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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: A050394 A156071 A005780 this_sequence A072331 A109518 A158119
Adjacent sequences: A033675 A033676 A033677 this_sequence 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 (njas(AT)research.att.com), Geoffrey Mess (mess(AT)math.ucla.edu)
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