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A035529
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A convolution triangle of numbers obtained from A034171.
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7
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1, 6, 1, 42, 12, 1, 315, 120, 18, 1, 2457, 1134, 234, 24, 1, 19656, 10458, 2673, 384, 30, 1, 160056, 95256, 28539, 5148, 570, 36, 1, 1320462, 861597, 292572, 62532, 8775, 792, 42, 1, 11003850, 7760610, 2920347, 713664, 119565, 13770, 1050, 48, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n,1)= A034171(n-1); a(n,m)=: s2(4; n,m), generalizing s2(2; n,m) := A007318(n-1,m-1) (Pascal), s2(3; n,m) := A035324(n,m).
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LINKS
| W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
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FORMULA
| a(n+1, m) = 3*(3*n+m)*a(n, m)/(n+1) + m*a(n, m-1)/(n+1), n >= m >= 1; a(n, m) := 0, n<m; a(n, 0) := 0; a(1, 1)=1; G.f. for column m: ((-1+(1-9*x)^(-1/3))/3)^m.
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EXAMPLE
| {1}; {6,1}; {42,12,1}; {315,120,18,1 ]; ...
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CROSSREFS
| Cf. A034171, A007318, A035324. Row sums: A049028(n), n >= 1.
Sequence in context: A113365 A145356 A145357 * A135893 A051338 A062138
Adjacent sequences: A035526 A035527 A035528 * A035530 A035531 A035532
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KEYWORD
| easy,nice,nonn,tabl
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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