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A241066 Array t(n,k) = k^(2n)*(k^(2n)-1)*BernoulliB(2n)/(2n), n>=1, k>=2, absolute values read by ascending antidiagonals. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Apr 16 2014

STATUS

approved

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Last modified October 24 09:09 EDT 2021. Contains 348220 sequences. (Running on oeis4.)