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A004141 Norm of a matrix.

%I A004141 M1876 #27 Oct 24 2023 20:26:34
%S A004141 1,2,8,48,256,1280,6912,39424,212992,1118208,6553600,36765696,
%T A004141 199229440,1133117440,6499598336,36175872000,200655503360,
%U A004141 1167945891840,6620826304512,36681168191488,212364657950720,1219998345330688,6864598984556544,38958828003262464,226089827240509440,1287455960675123200
%N A004141 Norm of a matrix.
%C A004141 Maximum in the row n-1 of the absolute values of the triangle A127674. - _R. J. Mathar_, Jul 15 2015
%D A004141 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A004141 D. W. Kammler and R. J. McGlinn, <a href="http://www.jstor.org/stable/2320150">Local conditioning of parametric forms used to approximate continuous functions</a>, Amer. Math. Monthly, 86 (1979), 841-845.
%H A004141 D. W. Kammler and R. J. McGlinn, <a href="/A004141/a004141.pdf">Local conditioning of parametric forms used to approximate continuous functions</a>, Amer. Math. Monthly, 86 (1979), 841-845. [Annotated scan of page 843 only]
%F A004141 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
%p A004141 A := proc(n,k)
%p A004141     2*n/(n+k)*binomial(n+k,n-k)*2^(2*k-1) ;
%p A004141 end proc:
%p A004141 A004141 := proc(n)
%p A004141     seq(abs(A(n,k)),k=0..n-1) ;
%p A004141     max(%) ;
%p A004141 end proc:
%p A004141 seq(A004141(n),n=1..30) ; # _R. J. Mathar_, Jul 15 2015
%t A004141 A[n_, k_] := 2n/(n+k) Binomial[n+k, n-k] 2^(2k-1);
%t A004141 row[n_] := Table[A[n, k], {k, 0, n-1}] // Abs;
%t A004141 a[n_] := If[n < 3, n, row[n-1] // Max];
%t A004141 Array[a, 30] (* _Jean-François Alcover_, Mar 30 2020, from Maple *)
%Y A004141 Cf. A259868.
%K A004141 nonn
%O A004141 1,2
%A A004141 _N. J. A. Sloane_