Search: id:A030524
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%I A030524
%S A030524 1,6,1,30,12,1,135,96,18,1,567,630,198,24,1,2268,3654,1701,336,30,1,
%T A030524 8748,19440,12501,3564,510,36,1,32805,96957,82296,31644,6435,720,42,1,
%U A030524 120285,459756,498663,247536,66915,10530,966,48,1,433026,2092959
%N A030524 A convolution triangle of numbers obtained from A036068.
%C A030524 a(n,m) := s1p(4; 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(4; n,m).
%H A030524 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.
%F A030524 a(n, m) = 3*(3*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*(1-3*x+3*x^2)/
               (1-3*x)^3)^m.
%e A030524 {1}; {6,1}; {30,12,1}; {135,96,18,1}; {567,630,198,24,1}; ...
%Y A030524 Cf. A030523, A043553. a(n, 1)= A036068(n-1). Row sums = A043553(n).
%Y A030524 Sequence in context: A046212 A120105 A120101 this_sequence A051930 A147320 
               A038255
%Y A030524 Adjacent sequences: A030521 A030522 A030523 this_sequence A030525 A030526 
               A030527
%K A030524 easy,nonn,tabl
%O A030524 1,2
%A A030524 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)

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