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A363351
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Number of n element multisets of length n vectors over GF(2) that sum to zero.
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2
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1, 1, 4, 15, 276, 11781, 1878976, 1025425687, 1991615557152, 13956142211859705, 356420795746828010496, 33403125520521519582574755, 11550847036800645994553295682560, 14809214844165378046279886451931058885, 70706990798105074752791720424861516970573824
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OFFSET
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0,3
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COMMENTS
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Number of equivalence classes of n X n binary matrices with an even number of 1's in each column under permutation of rows.
Number of equivalence classes of n X n binary matrices under permutation of rows and complementation of columns.
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LINKS
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FORMULA
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a(n) = binomial(2^n+n-1, n)/2^n for odd n;
a(n) = (binomial(2^n+n-1, n) + (2^n-1)*binomial(2^(n-1)+n/2-1, n/2))/2^n for even n.
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MATHEMATICA
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A363351[n_]:=(Binomial[2^n+n-1, n]+If[EvenQ[n], (2^n-1)Binomial[2^(n-1)+n/2-1, n/2], 0])/2^n; Array[A363351, 20, 0] (* Paolo Xausa, Nov 19 2023 *)
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PROG
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(PARI) a(n)={(binomial(2^n+n-1, n) + if(n%2==0, (2^n-1)*binomial(2^(n-1)+n/2-1, n/2)))/2^n}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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