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

Offset

0,2

Links

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

Example

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

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 *)

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.

Sequence in context: A239677 A331333 A120399 * A134812 A144847 A143625

Adjacent sequences: A144813 A144814 A144815 * A144817 A144818 A144819

Keyword

frac,nonn,tabl,look

Author

Alois P. Heinz, Sep 21 2008

Status

approved