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A092083
A convolution triangle of numbers obtained from A034789.
7
1, 21, 1, 546, 42, 1, 15561, 1533, 63, 1, 466830, 54054, 2961, 84, 1, 14471730, 1885338, 124740, 4830, 105, 1, 458960580, 65542932, 4977882, 236880, 7140, 126, 1, 14801478705, 2277656901, 192582117, 10661301, 399735, 9891, 147, 1
OFFSET
1,2
COMMENTS
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.
LINKS
W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
W. Lang, First 10 rows.
FORMULA
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.
EXAMPLE
{1}; {21,1}; {546,42,1}; {15561,1533,63,1}; ...
CROSSREFS
Cf. A092086 (row sums), A092087 (alternating row sums).
Sequence in context: A260531 A252939 A132166 * A040435 A040434 A040437
KEYWORD
nonn,easy,tabl
AUTHOR
Wolfdieter Lang, Mar 19 2004
STATUS
approved