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A093557
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Triangle of denominators of coefficients of Faulhaber polynomials in Knuth's version.
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6
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1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 6, 15, 3, 15, 30, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1, 2, 1, 1, 5, 2, 5, 10, 1, 1, 3, 2, 7, 1, 3, 42, 21, 21, 1, 1, 2, 3, 2, 1, 6, 15, 3, 5, 10, 1, 1, 1, 5, 3, 10, 5, 15, 5, 5, 1, 1, 1, 1, 6, 3, 2, 3, 3, 7, 1, 1, 14, 21, 42, 1, 1, 1, 2, 1, 1, 1, 1, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| The companion triangle with the numerators is A093556, where more information can be found.
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LINKS
| W. Lang, First 10 rows.
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FORMULA
| a(m, k)= denominator(A(m, k)) with recursion: A(m, 0)=1, A(m, k)=-(sum(binomial(m-j, 2*k+1-2*j)*A(m, j), j=0..k-1))/(m-k) if 0<= k <= m-1, else 0. From the 1993 Knuth reference, given in A093556, p. 288, eq.(*) with A^{(m)}_k = A(m, k).
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EXAMPLE
| [1]; [1,1]; [1,2,1]; [1,3,3,1]; ...
Denominators of [1]; [1,0]; [1,-1/2,0]; [1,-4/3,2/3,0]; ... (see W. Lang link in A093556.)
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MATHEMATICA
| a[m_, k_] := (-1)^(m-k)* Sum[ Binomial[2*m, m-k-j]*Binomial[m-k+j, j]*((m-k-j)/(m-k+j))*BernoulliB[m+k+j], {j, 0, m-k}]; Flatten[ Table[ Denominator[a[m, k]], {m, 1, 14}, {k, 0, m-1}]] (* From Jean-François Alcover, Oct 25 2011 *)
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CROSSREFS
| Sequence in context: A117185 A129181 A157694 * A098802 A048804 A158565
Adjacent sequences: A093554 A093555 A093556 * A093558 A093559 A093560
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KEYWORD
| nonn,frac,tabl,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Apr 02 2004
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