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A132057 A convolution triangle of numbers obtained from A034904.

%I A132057 #10 Aug 29 2019 16:30:00
%S A132057 1,28,1,980,56,1,37730,2744,84,1,1531838,130340,5292,112,1,64337196,
%T A132057 6136956,299782,8624,140,1,2766499428,288408120,16120314,568008,12740,
%U A132057 168,1,121034349975,13561837212,841627332,34401528,956970,17640,196,1
%N A132057 A convolution triangle of numbers obtained from A034904.
%C A132057 a(n,1) = A034904(n). a(n,m)=: s2(8; n,m), a member of a sequence of unsigned triangles including s2(2; n,m)=A007318(n-1,m-1) (Pascal's triangle). s2(3;n,m)= A035324(n,m), s2(4; n,m)= A035529(n,m), s2(5; n,m)= A048882(n,m), s2(6; n,m)= A049375; s2(7; n,m)=A092083.
%H A132057 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 A132057 W. Lang, <a href="/A132057/a132057.txt">First 10 rows</a>.
%F A132057 a(n, m) = 7*(7*(n-1)+m)*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.
%F A132057 G.f. for m-th column: ((-1+(1-49*x)^(-1/7))/7)^m.
%e A132057 {1}; {28,1}; {980,56,1}; (37730,2744,84,1);...
%t A132057 a[n_, m_] := a[n, m] = 7*(7*(n-1) + m)*a[n-1, m]/n + m*a[n-1, m-1]/n;
%t A132057 a[n_, m_] /; n < m = 0; a[_, 0] = 0; a[1, 1] = 1;
%t A132057 Flatten[Table[a[n, m], {n, 1, 8}, {m, 1, n}]][[1 ;; 36]]
%t A132057 (* _Jean-François Alcover_, Jun 17 2011 *)
%Y A132057 Cf. A132058 (row sums), A132059 (negative of alternating row sums).
%K A132057 nonn,easy,tabl
%O A132057 1,2
%A A132057 _Wolfdieter Lang_ Sep 14 2007