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Search: id:A132057
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| 1, 28, 1, 980, 56, 1, 37730, 2744, 84, 1, 1531838, 130340, 5292, 112, 1, 64337196, 6136956, 299782, 8624, 140, 1, 2766499428, 288408120, 16120314, 568008, 12740, 168, 1, 121034349975, 13561837212, 841627332, 34401528, 956970, 17640, 196, 1
(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,1) = A034904(n). a(n,m)=: s2(8; 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; s2(7; n,m)=A092083.
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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 10 rows.
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FORMULA
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a(n, m) = 7*(7*(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+(1-49*x)^(-1/7))/7)^m.
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EXAMPLE
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{1}; {28,1}; {980,56,1}; (37730,2744,84,1);...
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CROSSREFS
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Cf. A132058 (row sums), A132059 (negative of alternating row sums).
Adjacent sequences: A132054 A132055 A132056 this_sequence A132058 A132059 A132060
Sequence in context: A040810 A040811 A051000 this_sequence A040777 A036568 A040776
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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) Sep 14 2007
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