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A368761
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Number of labeled split graphs on n vertices such that {1..k} is independent and {k+1..n} is a clique for some k in {0..n}.
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0
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1, 2, 6, 24, 128, 928, 9280, 129152, 2515200, 68780544, 2647000064, 143580989440, 10988411686912, 1187350176604160, 181232621966082048, 39089521693818912768, 11916533065969825808384, 5135497592471003032846336, 3128995097443083790244380672, 26956139043, 12277811648715554816
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OFFSET
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1,2
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COMMENTS
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Also the number of sign mappings X:([n] choose 2) -> {+,-} such that for any ordered 3-tuple abc we have X(ab)X(ac)X(bc) not in {++-,+--}.
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LINKS
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FORMULA
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a(n) = 1 + Sum_{k=1..n-1} (2^k-1)*2^((n-1-k)*k).
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PROG
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(Python) def f(n): return 1+sum((2**k-1)*2**((n-1-k)*k) for k in range(1, 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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