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Search: id:A159749
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| A159749 |
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The decomposition of a certain labeled universe (A052584), triangle read by rows. |
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+0
2
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| 2, 2, 4, 2, 12, 16, 0, 24, 96, 96, -8, 0, 320, 960, 768, 0, -240, 0, 4800, 11520, 7680, 240, 0, -6720, 0, 80640, 161280, 92160, 0, 13440, 0, -188160, 0, 1505280, 2580480, 1290240, -24192, 0, 645120, 0, -5419008, 0, 30965760, 46448640, 20643840
(list; table; graph; listen)
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OFFSET
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0,1
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COMMENT
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T(n,k) is a weighted binomial sum of the Bernoulli numbers A027641/A027642 with A027641(1) = 1, which amounts to the definition B_{n} = B_{n}(1).
T(n,k) = (n+1)!*C(n,k)*B_{n-k}*2^(k+1)/(k+1).
T(n,n) is A066318(n+1) = n!*2^(n+1) (necklaces with n labeled beads of 2 colors; see also A032184).
Sum_{k=0..n} T(n,k) is A052584(n+1) = (n+1)!*(1+2^n).
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EXAMPLE
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2
2, 4
2, 12, 16
0, 24, 96, 96
-8, 0, 320, 960, 768
0, -240, 0, 4800, 11520, 7680
240, 0, -6720, 0, 80640, 161280, 92160
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MAPLE
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T := (n, k) -> (n+1)!*binomial(n, k)*bernoulli(n-k, 1)*2^(k+1)/(k+1);
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CROSSREFS
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Sequence in context: A010026 A059427 A126984 this_sequence A102416 A129243 A084896
Adjacent sequences: A159746 A159747 A159748 this_sequence A159750 A159751 A159752
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KEYWORD
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sign,tabl
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AUTHOR
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Peter Luschny (peter(AT)luschny.de), Apr 20 2009
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