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Array t(n,k) = k^(2n)*(k^(2n)-1)*BernoulliB(2n)/(2n), n>=1, k>=2, absolute values read by ascending antidiagonals.
2

%I #8 Apr 18 2014 01:30:17

%S 1,2,6,16,54,20,272,2106,544,50,7936,179334,66560,3250,105,353792,

%T 26414586,17895424,968750,13986,196,22368256,5957217414,8329625600,

%U 635781250,8637840,48020,336,1903757312,1906398972666,5937093935104,722480468750,11754617616,54925276,139776,540

%N Array t(n,k) = k^(2n)*(k^(2n)-1)*BernoulliB(2n)/(2n), n>=1, k>=2, absolute values read by ascending antidiagonals.

%C For any integers n and k, the ratio k^(2n)*(k^(2n)-1)*B(2n)/(2n) is always an integer.

%C Row 1 is A002415 = 4-D pyramidal numbers,

%C Row 2 and following rows are not in the OEIS,

%C Column 1 is A000182 = Tangent numbers,

%C Column 2 is A047681,

%C Column 3 is A047682,

%C Column 4 is A047683,

%C Column 5 and following columns are not in the OEIS.

%H MathWorld, <a href="http://mathworld.wolfram.com/BernoulliNumber.html">Bernoulli Number</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Bernoulli_number">Bernoulli number</a>

%e Array begins:

%e 1, 6, 20, 50, 105, ...

%e 2, 54, 544, 3250, 13986, ...

%e 16, 2106, 66560, 968750, 8637840, ...

%e 272, 179334, 17895424, 635781250, 11754617616, ...

%e 7936, 26414586, 8329625600, 722480468750, 27698169542400, ...

%e etc.

%t nmax = 8; t[n_, k_] := k^(2*n)*(k^(2*n)-1)*BernoulliB[2*n]/(2*n); Table[t[n-k+2, k] // Abs, {n, 1, nmax}, {k, 2, n+1}] // Flatten

%Y Cf. A000182, A002415, A047681, A047682, A047683.

%K nonn,tabl

%O 1,2

%A _Jean-François Alcover_, Apr 16 2014