A241066 Array t(n,k) = k^(2n)*(k^(2n)-1)*BernoulliB(2n)/(2n), n>=1, k>=2, absolute values read by ascending antidiagonals.

1, 2, 6, 16, 54, 20, 272, 2106, 544, 50, 7936, 179334, 66560, 3250, 105, 353792, 26414586, 17895424, 968750, 13986, 196, 22368256, 5957217414, 8329625600, 635781250, 8637840, 48020, 336, 1903757312, 1906398972666, 5937093935104, 722480468750, 11754617616, 54925276, 139776, 540

Offset: 1

Author

Jean-François Alcover, Apr 16 2014

Keywords

• nonn
• tabl

Comments

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

Row 1 is A002415 = 4-D pyramidal numbers,

Row 2 and following rows are not in the OEIS,

Column 1 is A000182 = Tangent numbers,

Column 2 is A047681,

Column 3 is A047682,

Column 4 is A047683,

Column 5 and following columns are not in the OEIS.

Examples

			Array begins:
   1,        6,         20,           50,            105, ...
   2,       54,        544,         3250,          13986, ...
  16,     2106,      66560,       968750,        8637840, ...
272,   179334,   17895424,    635781250,    11754617616, ...
7936, 26414586, 8329625600, 722480468750, 27698169542400, ...
etc.
		

Links

• MathWorld, Bernoulli Number
• Wikipedia, Bernoulli number

Crossrefs

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

Programs

Mathematica

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