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A136564
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Array read by rows: T(n,k) is the number of directed multigraphs with loops with n arcs, k vertices, and no vertex of degree 0.
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7
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1, 1, 1, 5, 4, 1, 1, 9, 21, 16, 4, 1, 1, 18, 71, 108, 71, 22, 4, 1, 1, 27, 194, 491, 557, 326, 101, 22, 4, 1, 1, 43, 476, 1903, 3353, 3062, 1587, 497, 111, 22, 4, 1, 1, 59, 1030, 6298, 16644, 22352, 17035, 7982, 2433, 555, 111, 22, 4, 1, 1, 84, 2095, 18823, 72064
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OFFSET
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1,4
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COMMENTS
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Length of the n^th row: 2n.
T(n,1) = 1 if n > 0.
T(n,2n) = 1 if n > 0.
T(n,2n-1) = 4 if n >= 2.
T(n,2n-k) = A144047(k) for n large enough (conjecturally, n >= 2k is enough).
Row sums: A052171.
Sums of the first 2 entries of each row: A005993.
Sums of the first 3 entries of each row: A050927.
Sums of the first 4 entries of each row: A050929.
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LINKS
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Table of n, a(n) for n=1..61.
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FORMULA
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T(n,2) = (n^3 + 6*n^2 + 11*n - 6)/12 + ((n+2)/4)[n even]. (the bracket means that the second term is added if and only if n is even). [Benoit Jubin, Mar 31 2012]
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CROSSREFS
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Sequence in context: A213658 A046575 A154739 * A136042 A166044 A190287
Adjacent sequences: A136561 A136562 A136563 * A136565 A136566 A136567
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KEYWORD
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nonn,tabf
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AUTHOR
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Benoit Jubin, Apr 14 2008
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EXTENSIONS
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More terms from Benoit Jubin and Vladeta Jovovic (vladeta(AT)eunet.yu), Sep 08 2008
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STATUS
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approved
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