A144816 Denominators of triangle T(n,k), n>=0, 0<=k<=n, read by rows: T(n,k) is the coefficient of x^(2*k+1) in polynomial t_n(x), used to define continuous and n times differentiable sigmoidal transfer functions.

1, 2, 2, 8, 4, 8, 16, 16, 16, 16, 128, 32, 64, 32, 128, 256, 256, 128, 128, 256, 256, 1024, 512, 1024, 256, 1024, 512, 1024, 2048, 2048, 2048, 2048, 2048, 2048, 2048, 2048, 32768, 4096, 8192, 4096, 16384, 4096, 8192, 4096, 32768, 65536, 65536, 16384, 16384, 32768, 32768, 16384, 16384, 65536, 65536

Offset: 0

Author

Alois P. Heinz, Sep 21 2008

Keywords

• frac
• nonn
• tabl
• look

Examples

			Triangle begins:
    1;
    2,  2;
    8,  4,  8;
   16, 16, 16, 16;
  128, 32, 64, 32, 128;
  ...
		

Links

• Alois P. Heinz, Rows n = 0..140, flattened

Crossrefs

See A144815 for more information on T(n,k).

Main diagonal and column k=0 gives A046161.

Column k=1 gives A101926(n-1) = 2^A101925(n-1) = 2^(A005187(n-1)+1).

Cf. A077070.

Programs

Maple

# Function T(n,k) defined in A144815.
seq(seq(denom(T(n,k)), k=0..n), n=0..10);

Mathematica

row[n_] := Module[{f, a, eq}, f = Function[x, Sum[a[2*k+1]*x^(2*k+1), {k, 0, n}]]; eq = Table[Derivative[k][f][1] == If[k == 0, 1, 0], {k, 0, n}]; Table[a[2*k+1], {k, 0, n}] /. Solve[eq] // First]; Table[row[n] // Denominator, {n, 0, 10}] // Flatten (* Jean-François Alcover, Feb 03 2014 *)