login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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-Fran├žois Alcover, Sep 13 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 17 22:42 EDT 2019. Contains 328134 sequences. (Running on oeis4.)