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A002724
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Number of inequivalent n X n binary matrices, where equivalence means permutations of rows or columns.
(Formerly M1801 N0711)
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38
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1, 2, 7, 36, 317, 5624, 251610, 33642660, 14685630688, 21467043671008, 105735224248507784, 1764356230257807614296, 100455994644460412263071692, 19674097197480928600253198363072, 13363679231028322645152300040033513414, 31735555932041230032311939400670284689732948
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OFFSET
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0,2
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COMMENTS
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Also, number of bipartite graphs with both partite sets of size n, one of which is marked. For connected bipartite graphs, see A363846. - Max Alekseyev, Jun 24 2023
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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A. Kerber, Experimentelle Mathematik, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 19 (1988), 77-83. [Annotated scanned copy]
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FORMULA
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a(n) = Sum_{1*s_1+2*s_2+...=n, 1*t_1+2*t_2+...=n} (fixA[s_1, s_2, ...;t_1, t_2, ...]/(1^s_1*s_1!*2^s_2*s_2!*...*1^t_1*t_1!*2^t_2*t_2!*...)) where fixA[...] = 2^Sum_{i, j>=1} (gcd(i, j)*s_i*t_j). - Christian G. Bower, Dec 18 2003
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MAPLE
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# See Marko Riedel link.
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MATHEMATICA
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b[n_, i_] := b[n, i] = If[n == 0, {0}, If[i < 1, {}, Union[Flatten[Table[ Function[{p}, p + j*x^i] /@ b[n - i*j, i - 1], {j, 0, n/i}]]]]];
g[n_, k_] := g[n, k] = Sum[Sum[2^Sum[Sum[GCD[i, j]*Coefficient[s, x, i]* Coefficient[t, x, j], {j, 1, Exponent[t, x]}], {i, 1, Exponent[s, x]}]/ Product[i^Coefficient[s, x, i]*Coefficient[s, x, i]!, {i, 1, Exponent[s, x]}]/Product[i^Coefficient[t, x, i]*Coefficient[t, x, i]!, {i, 1, Exponent[t, x]}], {t, b[n + k, n + k]}], {s, b[n, n]}];
A[n_, k_] := g[Min[n, k], Abs[n - k]];
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PROG
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CROSSREFS
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Cf. A002623, A002727, A006148, A002728, A002725, A052269, A052271, A052272, A091059, A363845, A363846, A000595.
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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a(15) from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 24 2008
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STATUS
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approved
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