A004141 Norm of a matrix. (Formerly M1876)

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

1,2

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

Table of n, a(n) for n=1..26.

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]

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

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 *)

Crossrefs

Cf. A259868.

Sequence in context: A356346 A292277 A173841 * A009693 A192251 A104190

Adjacent sequences: A004138 A004139 A004140 * A004142 A004143 A004144

Keyword

nonn

Author

N. J. A. Sloane

Status

approved