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

1,2

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.

Links

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

MathWorld, Bernoulli Number

Wikipedia, Bernoulli number

Example

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.

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

Crossrefs

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

Sequence in context: A263596 A263591 A218779 * A045696 A150028 A147730

Adjacent sequences: A241063 A241064 A241065 * A241067 A241068 A241069

Keyword

nonn,tabl

Author

Jean-François Alcover, Apr 16 2014

Status

approved