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 A229096 Triangle read by rows, whose row sums using Euler numbers are the unsigned even-indexed Bernoulli numbers (numerators). 1
 1, 1, 1, 5, 1, 5, 61, 5, 5, 61, 6925, 2135, 4375, 2135, 6925, 50521, 4155, 305, 305, 4155, 50521, 439985, 3890117, 7998375, 2005619, 7998375, 3890117, 439985, 199360981, 49190323, 50571521, 16913897, 16913897, 50571521, 49190323, 199360981 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 REFERENCES George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), p. 132. LINKS FORMULA T(n, k) = numerator(-(-1)^n*n*binomial(2n-2, 2k)*E(2k)*E(2n-2k-2)/(2^(2n-1)*(2^(2n)-1))), where with 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: 1; 1, 1; 5, 1, 5; 61, 5, 5, 61; 6925, 2135, 4375, 2135, 6925; 50521, 4155, 305, 305, 4155, 50521, 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 // Numerator CROSSREFS Cf. A229097(denominators), A002445, A000364, A000367. Sequence in context: A101692 A281105 A105060 * A290797 A200423 A176320 Adjacent sequences:  A229093 A229094 A229095 * A229097 A229098 A229099 KEYWORD nonn,frac,tabl AUTHOR Jean-François Alcover, Sep 13 2013 STATUS approved

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Last modified August 22 20:47 EDT 2019. Contains 326209 sequences. (Running on oeis4.)