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Search: id:A126853
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| A126853 |
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Table read by antidiagonals: B(n,m) is the numerator of the Bernoulli polynomial of order m and degree n evaluated at x=0. |
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1
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| 1, 0, 1, 0, -1, 1, 0, 1, -1, 1, 0, 0, 5, -3, 1, 0, -1, -1, 2, -2, 1, 0, 0, 1, -9, 11, -5, 1, 0, 1, 1, 19, -6, 35, -3, 1, 0, 0, -5, -3, 251, -25, 17, -7, 1, 0, -1, -1, -16, -9, 24, -45, 35, -4, 1, 0, 0, 7, 5, 221, -475, 274, -147, 46, -9, 1, 0, 5, 3, 19, 11, 4315, -120, 1624, -56, 39, -5, 1, 0, 0, -15, -63, -199, -475, 19087, -294, 967, -81
(list; table; graph; listen)
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OFFSET
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0,13
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COMMENT
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Absolute values of the diagonal are in A002657. Not to be confused with the poly-Bernoulli numbers.
Let H(k) = Sum_{i=1..k+1} 1/i. Then Seq((-1)^k*T(k,k+2),k=0..) = Seq(k!*H(k),k=0..) = 1,3/2,11/3,25/2,274/5,294,.. (Cf. A160039 and A014973) [From Peter Luschny (peter(AT)luschny.de), Apr 30 2009]
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LINKS
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D. Cvijovic and H. M. Srivastava, Closed form summation of the Dowker and related sums, J. Math. Phys. 48 (2007) 043507.
Index entries for sequences realted to Bernoulli numbes.
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FORMULA
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E.g.f.: [t/(exp(t)-1)]^m*exp(t*x)=sum_{n=0..infinity} B_n^m(x)*t^n/n!.
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EXAMPLE
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Table of fractions B(n,m) is read along antidiagonals and starts in row n=0 and column m=0:
1, 1, 1, 1, 1, 1, 1, 1, ...
0, -1/2, -1, -3/2, -2, -5/2, -3, -7/2, ...
0, 1/6, 5/6, 2, 11/3, 35/6, 17/2, 35/3, ...
0, 0, -1/2, -9/4, -6, -25/2, -45/2, -147/4, ...
0, -1/30, 1/10, 19/10, 251/30, 24, 274/5, 1624/15, ...
0, 0, 1/6, -3/4, -9, -475/12, -120, -294, ...
0, 1/42, -5/42, -16/21, 221/42, 4315/84, 19087/84, 720, ...
0, 0, -1/6, 5/4, 11/3, -475/12, -1375/4, -36799/24, ...
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CROSSREFS
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Sequence in context: A077602 A144481 A065469 this_sequence A132199 A111142 A159671
Adjacent sequences: A126850 A126851 A126852 this_sequence A126854 A126855 A126856
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KEYWORD
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frac,sign,tabl
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AUTHOR
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R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 13 2007, May 17 2007
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