0,2

H. S. Wilf, Generatingfunctionology, Academic Press, NY, 1990, p. 79, Eq. 3.11.2.

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

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

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

Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

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

H. S. Wilf, Generatingfunctionology, 2nd edn., Academic Press, NY, 1994, p. 88, Eq. 3.11.2.

Sum(binomial(n, k)*2^(k*(n-k)), k=0..n).

E.g.f. A(x) = Sum_{n>=0} exp(2^n*x)*x^n/n!. - Paul D. Hanna (pauldhanna(AT)juno.com), Nov 27 2007

O.g.f.: A(x) = Sum_{n>=0} x^n/(1 - 2^n*x)^(n+1). - Paul D. Hanna (pauldhanna(AT)juno.com), Mar 08 2008

For n=2, {1,2 black, not connected}, {1,2 white, not connected}, {1 black, 2 white, not connected}, {1 black, 2 white, connected}, {1 white, 2 black, not connected}, {1 white, 2 black, connected}

(PARI) {a(n)=n!*polcoeff(sum(k=0, n, exp(2^k*x +x*O(x^n))*x^k/k!), n)} - Paul D. Hanna (pauldhanna(AT)juno.com), Nov 27 2007

(PARI) {a(n)=polcoeff(sum(k=0, n, x^k/(1-2^k*x +x*O(x^n))^(k+1)), n)} - Paul D. Hanna (pauldhanna(AT)juno.com), Mar 08 2008

Cf. A001831, A002031, A052332.

Cf. A135079 (variant).

a(n)=4*A000683(n)+2 - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 02 2000.

Sequence in context: A112934 A135922 A103367 this_sequence A141713 A005272 A002449

Adjacent sequences: A047860 A047861 A047862 this_sequence A047864 A047865 A047866

nonn,nice

N. J. A. Sloane (njas(AT)research.att.com).

Better description from Christian G. Bower (bowerc(AT)usa.net), Dec 15 1999.