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Search: id:A132166
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| 1, 21, 1, 336, 42, 1, 4536, 1113, 63, 1, 54432, 23184, 2331, 84, 1, 598752, 412272, 65205, 3990, 105, 1, 6158592, 6531840, 1518048, 139860, 6090, 126, 1, 60046272, 94618368, 30912840, 4010769, 256410, 8631, 147, 1, 560431872, 1274921856
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Signed version: (-1)^(n-m)*a(n, m) := s1(7; n,m).
a(n,m) := s1p(7; n,m), a member of a sequence of unsigned triangles including s1p(2; n,m)= A007318(n-1,m-1) (Pascal's triangle), A030523=s1p(3), A036068=s1p(4), A030526=s1p(5) and A030527=s1p(6).
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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.
W. Lang, First ten rows.
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FORMULA
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a(n, m) = 6*(6*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: ((1-(1-6*x)^6)/(36*(1-6*x)^6))^m.
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EXAMPLE
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{1};{21,1};{336,42,1};{4536,1113,63,1};...; Row polynomial s(3,x)=336*x+42*x^2+x^3.
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CROSSREFS
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Related triangle A134141 (S1p(7)).
Cf. A036224(n-1), n>=1 (first column). A132167 (row sums). A132168 (alternating row sums).
Sequence in context: A040459 A040460 A040461 this_sequence A092083 A013530 A013531
Adjacent sequences: A132163 A132164 A132165 this_sequence A132167 A132168 A132169
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Oct 12 2007
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