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A047864 Number of labeled bipartite graphs with n nodes. 14
1, 1, 2, 7, 41, 376, 5177, 103237, 2922446, 116011231, 6433447397, 498234407452, 54007795331921, 8213123246906761, 1756336596363006842, 528975889250504033527, 224688018516023267969441, 134708289561117007261966816 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
REFERENCES
Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, p. 406.
H. S. Wilf, Generatingfunctionology, Academic Press, NY, 1990, p. 80, Eq. 3.11.5.
LINKS
Vladislav Bína and Jiří Přibil, Note on enumeration of labeled split graphs, Comment. Math. Univ. Carolin. 56,2 (2015) 133-137.
S. R. Finch, Bipartite, k-colorable and k-colored graphs, June 5, 2003. [Cached copy, with permission of the author]
Eric Weisstein's World of Mathematics, n-Colorable Graph.
H. S. Wilf, Generatingfunctionology, 2nd edn., Academic Press, NY, 1994, p. 89, Eq. 3.11.5.
FORMULA
E.g.f.: sqrt( e.g.f. for A047863 ).
MATHEMATICA
nn = 20; a = Sum[Sum[Binomial[n, k] 2^(k (n - k)), {k, 0, n}] x^n/n!, {n, 0, nn}]; Range[0, nn]! CoefficientList[Series[a^(1/2), {x, 0, nn}], x] (* Geoffrey Critzer, Jan 15 2012 *)
PROG
(PARI) N=18; x='x+O('x^N); Vec(serlaplace(sqrt(sum(n=0, N, exp(2^n*x)*x^n/n!)))) \\ Gheorghe Coserea, Nov 13 2017
CROSSREFS
Row sums of A117279.
The unlabeled version is A033995.
Sequence in context: A113144 A320415 A006846 * A173916 A163921 A213434
KEYWORD
nonn,nice,easy
AUTHOR
STATUS
approved

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Last modified July 12 23:06 EDT 2024. Contains 374257 sequences. (Running on oeis4.)