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0, 1, 1, 1, 0, -1, 0, 1, 0, -3, 0, 5, 0, -691, 0, 35, 0, -3617, 0, 43867, 0, -1222277, 0, 854513, 0, -1181820455, 0, 76977927, 0, -23749461029, 0, 8615841276005, 0, -84802531453387, 0, 90219075042845, 0
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OFFSET
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0,10
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COMMENTS
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Numerators of Br(n) = 0, 1, 1, 1/2, 0, -1/6, 0, 1/6, 0, -3/10, 0, 5/6, 0, -691/210,... complementary Bernoulli numbers.
A164555(n)/A027642(n) is an autosequence of second kind. Its inverse binomial transform is the signed sequence and its main diagonal is the double of the first upper diagonal.
Br(n) is an autosequence of first kind. Its inverse binomial transform is the signed sequence and its main diagonal is A000004=0's.
Br(n) difference table:
0, 1, 1, 1/2, 0, -1/6,...
-1, -1/2, 0, 1/3, 1/3, 0,...
1/2, 1/2, 1/3, 0, -1/3, -1/3,...
0, -1/6, -1/3, -1/3, 0, 8/15,...
-1/6, -1/6, 0, 1/3, 8/15, 0,... etc.
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LINKS
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FORMULA
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a(n) = numerators of n * b(n) with b(n)=0 followed by A164555(n)/A027642(n) = 0, 1, 1/2, 1/6, 0,... in A165142(n).
a(n+1) = numerators of Br(n+1) = Br(n) + A140351(n)/A140219(n), a(0)=Br(0)=0.
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MATHEMATICA
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a[0] = 0; a[1] = a[2] = 1; a[n_] := 2*n*BernoulliB[n-1] // Numerator; Table[a[n], {n, 0, 36}] (* Jean-François Alcover, Nov 25 2013 *)
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CROSSREFS
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Cf. A050925: a similar sequence, because 2*(n+1)*B(n) and (n+1)*B(n) have the same numerator.
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KEYWORD
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sign,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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