Search: id:A030523
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%I A030523
%S A030523 1,3,1,8,6,1,20,25,9,1,48,88,51,12,1,112,280,231,86,15,1,256,832,912,
%T A030523 476,130,18,1,576,2352,3276,2241,850,183,21,1,1280,6400,10976,9424,
%U A030523 4645,1380,245,24,1,2816,16896,34848,36432,22363,8583,2093,316,27,1
%N A030523 A convolution triangle of numbers obtained from A001792.
%C A030523 a(n,m) := s1p(3; n,m), a member of a sequence of unsigned triangles including 
               s1p(2; n,m)= A007318(n-1,m-1) (Pascal's triangle). Signed version: 
               (-1)^(n-m)*a(n,m) := s1(3; n,m).
%C A030523 With offset 0, this is T(n,k)=sum{i=0..n, C(n,i)C(i+k+1,2k+1)}. Binomial 
               transform of A078812 (product of lower triangular matrices). - Paul 
               Barry (pbarry(AT)wit.ie), Jun 22 2004
%H A030523 W. Lang, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               On generalizations of Stirling number triangles</a>, J. Integer Seqs., 
               Vol. 3 (2000), #00.2.4.
%H A030523 W. Lang, <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A030523.text">
               First ten rows. </a>
%F A030523 a(n, m) = 2*(2*m+n-1)*a(n-1, m)/n + m*a(n-1, m-1)/n, n >= m >= 1; a(n, 
               m) := 0, n<m; a(n, 0) := 0; a(1, 1)=1. G.f. for m-th column: (x*(1-x)/
               (1-2*x)^2)^m.
%e A030523 {1}; {3,1}; {8,6,1}; {20,25,9,1}; {48,88,51,12,1}; ...
%Y A030523 a(n, 1)= A001792(n-1). Row sums = A039717(n).
%Y A030523 Cf. A057682 (alternating row sums).
%Y A030523 Sequence in context: A016477 A062196 A103247 this_sequence A123965 A124025 
               A125662
%Y A030523 Adjacent sequences: A030520 A030521 A030522 this_sequence A030524 A030525 
               A030526
%K A030523 easy,nonn,tabl
%O A030523 1,2
%A A030523 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)

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