A092083 - OEIS

%I #10 Aug 28 2019 17:09:29

%S 1,21,1,546,42,1,15561,1533,63,1,466830,54054,2961,84,1,14471730,

%T 1885338,124740,4830,105,1,458960580,65542932,4977882,236880,7140,126,

%U 1,14801478705,2277656901,192582117,10661301,399735,9891,147,1

%N A convolution triangle of numbers obtained from A034789.

%C a(n,1) = A034789(n). a(n,m)=: s2(7; 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.

%H 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 W. Lang, <a href="/A092083/a092083.txt">First 10 rows</a>.

%F a(n, m) = 6*(6*(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. G.f. for m-th column: ((-1+(1-36*x)^(-1/6))/6)^m.

%e {1}; {21,1}; {546,42,1}; {15561,1533,63,1}; ...

%Y Cf. A092086 (row sums), A092087 (alternating row sums).

%K nonn,easy,tabl

%O 1,2

%A _Wolfdieter Lang_, Mar 19 2004