A229097 Triangle read by rows, whose row sums using Euler numbers are the unsigned even-indexed Bernoulli numbers (denominators).

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

Offset

1,1

References

George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), p. 132.

Links

Table of n, a(n) for n=1..29.

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