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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

Table of n, a(n) for n=1..36.

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-Fran├žois Alcover, Sep 13 2013

STATUS

approved

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