A004141 Norm of a matrix.

1, 2, 8, 48, 256, 1280, 6912, 39424, 212992, 1118208, 6553600, 36765696, 199229440, 1133117440, 6499598336, 36175872000, 200655503360, 1167945891840, 6620826304512, 36681168191488, 212364657950720, 1219998345330688, 6864598984556544, 38958828003262464, 226089827240509440, 1287455960675123200

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Maximum in the row n-1 of the absolute values of the triangle A127674. - R. J. Mathar, Jul 15 2015

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• D. W. Kammler and R. J. McGlinn, Local conditioning of parametric forms used to approximate continuous functions, Amer. Math. Monthly, 86 (1979), 841-845.
• D. W. Kammler and R. J. McGlinn, Local conditioning of parametric forms used to approximate continuous functions, Amer. Math. Monthly, 86 (1979), 841-845. [Annotated scan of page 843 only]

Crossrefs

Cf. A259868.

Programs

Maple

A := proc(n,k)
    2*n/(n+k)*binomial(n+k,n-k)*2^(2*k-1) ;
end proc:
A004141 := proc(n)
    seq(abs(A(n,k)),k=0..n-1) ;
    max(%) ;
end proc:
seq(A004141(n),n=1..30) ; # R. J. Mathar, Jul 15 2015

Mathematica

A[n_, k_] := 2n/(n+k) Binomial[n+k, n-k] 2^(2k-1);
row[n_] := Table[A[n, k], {k, 0, n-1}] // Abs;
a[n_] := If[n < 3, n, row[n-1] // Max];
Array[a, 30] (* Jean-François Alcover, Mar 30 2020, from Maple *)

Formula

The scanned page from Kammler and McGlinn (page 843 of the article) gives a fairly explicit way to calculate a(n). - N. J. A. Sloane, Jul 09 2015