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 A093557 Triangle of denominators of coefficients of Faulhaber polynomials in Knuth's version. 7
 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; text; internal format)
 OFFSET 1,5 COMMENTS The companion triangle with the numerators is A093556, where more information can be found. REFERENCES Askar Dzhumadildaev and Damir Yeliussizov, "Power Sums of Binomial Coefficients", Journal of Integer Sequences, Vol. 16 (2013), #13.1.1. D. Yeliussizov, Permutation Statistics on Multisets, Ph.D. Dissertation, Computer Science, Kazakh-British Technical University, 2012; http://www.kazntu.kz/sites/default/files/20121221ND_Eleusizov.pdf. LINKS W. Lang, First 10 rows. 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). 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.) 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}]] (* Jean-François Alcover, Oct 25 2011 *) CROSSREFS Sequence in context: A129181 A157694 A271187 * A098802 A048804 A158565 Adjacent sequences:  A093554 A093555 A093556 * A093558 A093559 A093560 KEYWORD nonn,frac,tabl,easy AUTHOR Wolfdieter Lang, Apr 02 2004 STATUS approved

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Last modified January 19 22:19 EST 2019. Contains 319310 sequences. (Running on oeis4.)