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A049375 A convolution triangle of numbers obtained from A034687.

%I A049375 #13 Nov 21 2013 13:11:31
%S A049375 1,15,1,275,30,1,5500,775,45,1,115500,19250,1500,60,1,2502500,471625,
%T A049375 44625,2450,75,1,55412500,11495000,1254000,85000,3625,90,1,1246781250,
%U A049375 279675000,34093125,2698875,143750,5025,105,1,28398906250,6802812500
%N A049375 A convolution triangle of numbers obtained from A034687.
%C A049375 a(n,1) = A034687(n). a(n,m)=: s2(6; 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).
%H A049375 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 A049375 a(n, m) = 5*(5*(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 A049375 G.f. for m-th column: ((-1+(1-25*x)^(-1/5))/5)^m.
%e A049375 {1}; {15,1}; {275,30,1}; {5500,775,45,1}; ...
%t A049375 a[n_, m_] := Coefficient[Series[((-1 + (1 - 25*x)^(-1/5))/5)^m, {x, 0, n}], x^n];
%t A049375 Flatten[Table[a[n, m], {n, 1, 9}, {m, 1, n}]][[1 ;; 38]]
%t A049375 (* _Jean-François Alcover_, Jun 21 2011, after g.f. *)
%Y A049375 Cf. A039746.
%K A049375 easy,nonn,tabl
%O A049375 1,2
%A A049375 _Wolfdieter Lang_