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A047864 Number of labeled bipartite graphs with n nodes. 12
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

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

S. R. Finch, Bipartite, k-colorable and k-colored graphs, June 5, 2003. [Cached copy, with permission of the author]

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

Sequence in context: A113144 A320415 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 August 18 07:10 EDT 2019. Contains 326072 sequences. (Running on oeis4.)