OFFSET
1,1
REFERENCES
George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), p. 132.
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
KEYWORD
AUTHOR
Jean-François Alcover, Sep 13 2013
STATUS
approved