A047864 Number of labeled bipartite graphs with n nodes.

1, 1, 2, 7, 41, 376, 5177, 103237, 2922446, 116011231, 6433447397, 498234407452, 54007795331921, 8213123246906761, 1756336596363006842, 528975889250504033527, 224688018516023267969441, 134708289561117007261966816

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

Row sums of A117279.

The unlabeled version is A033995.

Cf. A001832.

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