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Search: id:A048966
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| 1, 3, 1, 15, 6, 1, 90, 39, 9, 1, 594, 270, 72, 12, 1, 4158, 1953, 567, 114, 15, 1, 30294, 14580, 4482, 1008, 165, 18, 1, 227205, 111456, 35721, 8667, 1620, 225, 21, 1, 1741905, 867834, 287199, 73656, 15075, 2430, 294, 24, 1, 13586859, 6857136
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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A generalization of the Catalan triangle A033184.
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LINKS
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W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
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FORMULA
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a(n, m) = 3*(3*(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-(1-9*x)^(1/3))/3)^m.
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CROSSREFS
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Cf. A034000, A049213, A049223, A049224. a(n, 1)= A025748(n), a(n, 1)= 3^(n-1)*2*A034000(n-1)/n!, n >= 2. Row sums = A025756.
Adjacent sequences: A048963 A048964 A048965 this_sequence A048967 A048968 A048969
Sequence in context: A126454 A065250 A092589 this_sequence A104990 A089463 A136231
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KEYWORD
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easy,nonn,tabl,nice
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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