A297008 Number of edge covers in the complete tripartite graph K_n,n,n.

4, 2902, 117207580, 268752741193822, 37231937318464496521924, 323097476641999571450657507823382, 178177528846515370073473806783721111760309500, 6274803675843247716007930604166972482973014660984656159102

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..25

Eric Weisstein's World of Mathematics, Complete Tripartite Graph

Eric Weisstein's World of Mathematics, Edge Cover

Mathematica

b[m_, n_] := Sum[(-1)^j*Binomial[m, j]*If[n == 0, 1, (2^(m - j) - 1)^n], {j, 0, m}];
c[n_, s_] := Sum[Binomial[n, k]*Binomial[n, s - k]*b[k, s - k], {k, Max[0, s - n], Min[n, s]}];
a[n_] := Sum[c[n, 2*n - i]*Sum[(-1)^j*Binomial[i, j]*(2^(2*n - j) - 1)^n, {j, 0, i}], {i, 0, 2 n}];
Array[a, 10] (* Jean-François Alcover, Dec 27 2017, after Andrew Howroyd *)

Prog

(PARI) \\ here b(m, n) is A183109.
b(m, n)={sum(j=0, m, (-1)^j*binomial(m, j)*(2^(m - j) - 1)^n)}
c(n, s)={sum(k=max(0, s-n), min(n, s), binomial(n, k)*binomial(n, s-k)*b(k, s-k))}
a(n)={sum(i=0, 2*n, c(n, 2*n-i)*sum(j=0, i, (-1)^j*binomial(i, j)*(2^(2*n - j) - 1)^n))} \\ Andrew Howroyd, Dec 24 2017

Crossrefs

Cf. A048291, A183109.

Sequence in context: A066850 A066837 A275683 * A349074 A347605 A306728

Adjacent sequences: A297005 A297006 A297007 * A297009 A297010 A297011

Keyword

nonn

Author

Eric W. Weisstein, Dec 23 2017

Extensions

Terms a(4) and beyond from Andrew Howroyd, Dec 24 2017

Status

approved