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A297008
Number of edge covers in the complete tripartite graph K_{n,n,n}.
2
4, 2902, 117207580, 268752741193822, 37231937318464496521924, 323097476641999571450657507823382, 178177528846515370073473806783721111760309500, 6274803675843247716007930604166972482973014660984656159102
OFFSET
1,1
LINKS
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
Sequence in context: A066850 A066837 A275683 * A349074 A347605 A306728
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Dec 23 2017
EXTENSIONS
Terms a(4) and beyond from Andrew Howroyd, Dec 24 2017
STATUS
approved