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A245069
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Number of Markov blanket structures with n labeled nodes.
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1
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1, 3, 15, 153, 3567, 196833, 25604415, 7727833473, 5321887813887, 8241841773665793, 28359559029362676735, 214672167825864945784833, 3545389677599343390373285887, 126865139766788531002690137546753, 9777654677248888055040528691642187775
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OFFSET
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1,2
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LINKS
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FORMULA
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a(1) = 1; for n > 1, a(n) = Sum_{q=0..n-1} Sum_{r=0..n-q-1} ((n-1)!/(q!*r!*s!))*2^(q*s)*2^(r*s) * A003024(s); n-1=q+r+s.
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MATHEMATICA
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(* b = A003024 *) b[0] = b[1] = 1; b[n_] := b[n] = Sum[-(-1)^k Binomial[n, k] 2^(k(n-k)) b[n-k], {k, 1, n}];
a[n_] := Sum[Sum[s = n-q-r-1; ((n-1)!/(q! r! s!)) 2^(q s) 2^(r s) b[s], {r, 0, n-q-1}], {q, 0, n 1}];
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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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