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A047864 Number of labeled bipartite graphs with n nodes. 10
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, Handbook of Enumerative Combinatorics, CRC Press, 2015, p.406.

H. S. Wilf, Generatingfunctionology, Academic Press, NY, 1990, p. 80, Eq. 3.11.5.

LINKS

T. D. Noe, Table of n, a(n) for n=0..50

Vladislav Bína, Jiří Přibil, Note on enumeration of labeled split graphs, Comment. Math. Univ. Carolin. 56,2 (2015) 133 -137.

H. S. Wilf, Generatingfunctionology, 2nd edn., Academic Press, NY, 1994, p. 89, Eq. 3.11.5.

Eric Weisstein's World of Mathematics, n-Colorable Graph

S. R. Finch, Bipartite, k-colorable and k-colored graphs

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 *)

CROSSREFS

Sequence in context: A101390 A113144 A006846 * A173916 A163921 A213434

Adjacent sequences:  A047861 A047862 A047863 * A047865 A047866 A047867

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified September 2 17:53 EDT 2015. Contains 261289 sequences.