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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. 3
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Rows n = 0..44, 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-Fran├žois Alcover, Feb 03 2014 *)

CROSSREFS

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

Diagonal and column k=0 gives A046161.

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

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

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Last modified June 16 14:09 EDT 2021. Contains 345057 sequences. (Running on oeis4.)