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Search: id:A030523
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| 1, 3, 1, 8, 6, 1, 20, 25, 9, 1, 48, 88, 51, 12, 1, 112, 280, 231, 86, 15, 1, 256, 832, 912, 476, 130, 18, 1, 576, 2352, 3276, 2241, 850, 183, 21, 1, 1280, 6400, 10976, 9424, 4645, 1380, 245, 24, 1, 2816, 16896, 34848, 36432, 22363, 8583, 2093, 316, 27, 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,m) := s1p(3; 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(3; n,m).
With offset 0, this is T(n,k)=sum{i=0..n, C(n,i)C(i+k+1,2k+1)}. Binomial transform of A078812 (product of lower triangular matrices). - Paul Barry (pbarry(AT)wit.ie), Jun 22 2004
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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) = 2*(2*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-x)/(1-2*x)^2)^m.
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EXAMPLE
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{1}; {3,1}; {8,6,1}; {20,25,9,1}; {48,88,51,12,1}; ...
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CROSSREFS
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a(n, 1)= A001792(n-1). Row sums = A039717(n).
Cf. A057682 (alternating row sums).
Sequence in context: A016477 A062196 A103247 this_sequence A123965 A124025 A125662
Adjacent sequences: A030520 A030521 A030522 this_sequence A030524 A030525 A030526
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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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