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A109345
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a(n) = 5^((n^2 - n)/2).
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10
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1, 1, 5, 125, 15625, 9765625, 30517578125, 476837158203125, 37252902984619140625, 14551915228366851806640625, 28421709430404007434844970703125
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OFFSET
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0,3
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COMMENTS
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Sequence given by the Hankel transform (see A001906 for definition) of A078009 = {1, 1, 6, 41, 306, 2426, 20076, 171481, ...}; example: det([1, 1, 6, 41; 1, 6, 41, 306; 6, 41, 306, 2426; 41, 306, 2426, 20076]) = 5^6 = 15625.
a(n) is the number of simple labeled graphs, with bi-directional and non-directed edges allowed and not regarded as equivalent, on n labeled nodes. - Mark Stander, Feb 07 2019
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LINKS
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FORMULA
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a(n+1) is the determinant of n X n matrix M_(i, j) = binomial(5i, j).
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MAPLE
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MATHEMATICA
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PROG
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(Magma) [5^Binomial(n, 2): n in [0..12]]; // G. C. Greubel, Feb 09 2019
(Sage) [5^binomial(n, 2) for n in (0..12)] # G. C. Greubel, Feb 09 2019
(GAP) List([0..12], n -> 5^Binomial(n, 2)); # G. C. Greubel, Feb 09 2019
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CROSSREFS
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Cf. A006125 (number of graphs on n labeled nodes), A047656 (number of semi-complete digraphs on n labeled nodes), A053763 (number of simple digraphs on n labeled nodes), A053764.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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