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 A093559 Triangle of denominators of coefficients of Faulhaber polynomials used for sums of even powers. 4
 6, 10, 30, 14, 14, 42, 18, 9, 10, 30, 22, 33, 66, 22, 66, 26, 26, 78, 273, 910, 2730, 30, 30, 15, 9, 90, 2, 6, 34, 51, 51, 51, 102, 51, 170, 510, 38, 19, 95, 95, 190, 57, 3990, 266, 798, 42, 14, 7, 21, 6, 66, 1386, 693, 110, 330, 46, 138, 46, 23, 230, 690, 345, 23, 230, 46 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS The companion triangle with the numerators is A093558. See comment there. REFERENCES Askar Dzhumadildaev and Damir Yeliussizov, "Power Sums of Binomial Coefficients", Journal of Integer Sequences, Vol. 16 (2013), #13.1.1. D. E. Knuth, Johann Faulhaber and sums of powers, Maths. of Computation 61, 203 (1993) 277-294. Ivo Schneider, Johannes Faulhaber 1580-1635, Birkhäuser Verlag, Basel, Boston, Berlin, 1993, ch. 7, pp. 131-159. 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.-From N. J. A. Sloane, Jan 03 2013 LINKS FORMULA a(n, m) = denominator(Fe(m, k), with Fe(m, k):=(m-k)*A(m, k)/(2*m*(2*m-1)) with Faulhaber numbers A(m, k):=A093556(m, k)/A093557(m, k) in Knuth's version. From the bottom of p. 288 of the 1993 Knuth reference. EXAMPLE [6]; [10,30]; [14,14,42]; [18,9,10,30]; ... Denominators of [1/6]; [1/10,-1/30]; [1/14,-1/14,1/42]; [1/18,-1/9,1/10,-1/30]; ... (see W. Lang link in A093558.) 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}]; t[m_, k_] := (m-k)*a[m, k]/(2*m*(2*m-1)); Table[t[m, k] // Denominator, {m, 2, 12}, {k, 0, m-2}] // Flatten (* Jean-François Alcover, Mar 03 2014 *) CROSSREFS Sequence in context: A240972 A103767 A025129 * A269697 A271067 A271600 Adjacent sequences:  A093556 A093557 A093558 * A093560 A093561 A093562 KEYWORD nonn,frac,tabl,easy AUTHOR Wolfdieter Lang, Apr 02 2004 STATUS approved

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Last modified November 20 23:03 EST 2018. Contains 317427 sequences. (Running on oeis4.)