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Search: id:A030524
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| 1, 6, 1, 30, 12, 1, 135, 96, 18, 1, 567, 630, 198, 24, 1, 2268, 3654, 1701, 336, 30, 1, 8748, 19440, 12501, 3564, 510, 36, 1, 32805, 96957, 82296, 31644, 6435, 720, 42, 1, 120285, 459756, 498663, 247536, 66915, 10530, 966, 48, 1, 433026, 2092959
(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(n,m) := s1p(4; n,m), a member of a sequence of unsigned triangles including s1p(2; n,m)= A007318(n-1,m-1) (Pascal's triangle). Signed version: (-1)^(n-m)*a(n,m) := s1(4; n,m).
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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*m+n-1)*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: (x*(1-3*x+3*x^2)/(1-3*x)^3)^m.
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EXAMPLE
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{1}; {6,1}; {30,12,1}; {135,96,18,1}; {567,630,198,24,1}; ...
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CROSSREFS
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Cf. A030523, A043553. a(n, 1)= A036068(n-1). Row sums = A043553(n).
Sequence in context: A046212 A120105 A120101 this_sequence A051930 A147320 A038255
Adjacent sequences: A030521 A030522 A030523 this_sequence A030525 A030526 A030527
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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