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 A229097 Triangle read by rows, whose row sums using Euler numbers are the unsigned even-indexed Bernoulli numbers (denominators). 1
 6, 60, 60, 672, 112, 672, 8160, 544, 544, 8160, 523776, 130944, 261888, 130944, 523776, 1397760, 93184, 6656, 6656, 93184, 1397760, 3121152, 22368256, 44736512, 11184128, 44736512, 22368256, 3121152, 268431360 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), p. 132. LINKS FORMULA T(n, k) = denominator(-(-1)^n*n*binomial(2n-2, 2k)*E(2k)*E(2n-2k-2)/(2^(2n-1)*(2^(2n)-1))), where E(.) = Euler number. EXAMPLE 1/6; 1/60,         1/60; 5/672,        1/112,        5/672; 61/8160,      5/544,        5/544,        61/8160; 6925/523776,  2135/130944,  4375/261888,  2135/130944,  6925/523776; ... Row sums are 1/6, 1/30, 1/42, 1/30, 5/66, ... From Bruno Berselli, Sep 14 2013: (Start) Triangle begins: 6; 60, 60; 672, 112, 672; 8160, 544, 544, 8160; 523776, 130944, 261888, 130944, 523776; 1397760, 93184, 6656, 6656, 93184, 1397760; 3121152, 22368256, 44736512, 11184128, 44736512, 22368256, 3121152, etc. (End) MATHEMATICA t[n_, k_] := -(-1)^n n Binomial[2 n - 2, 2 k] EulerE[2 k] EulerE[2 n - 2 k - 2]/(2^(2 n - 1) (2^(2 n) - 1)); Table[t[n, k], {n, 1, 8}, {k, 0, n - 1}] // Flatten // Denominator CROSSREFS Cf. A229096 (numerators), A002445, A000364, A000367. Sequence in context: A024271 A271964 A237576 * A217399 A098185 A173904 Adjacent sequences:  A229094 A229095 A229096 * A229098 A229099 A229100 KEYWORD nonn,frac,tabl AUTHOR Jean-François Alcover, Sep 13 2013 STATUS approved

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Last modified September 22 21:07 EDT 2020. Contains 337291 sequences. (Running on oeis4.)