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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-François 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.)