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Search: id:A049324
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| A049324 |
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A convolution triangle of numbers generalizing Pascal's triangle A007318. |
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+0
5
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| 1, 3, 1, 3, 6, 1, 0, 15, 9, 1, 0, 18, 36, 12, 1, 0, 9, 81, 66, 15, 1, 0, 0, 108, 216, 105, 18, 1, 0, 0, 81, 459, 450, 153, 21, 1, 0, 0, 27, 648, 1305, 810, 210, 24, 1, 0, 0, 0, 594, 2673, 2970, 1323, 276, 27, 1, 0, 0, 0, 324, 3915, 7938
(list; table; graph; listen)
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OFFSET
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1,2
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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*p(2, x))^m, p(2, x) := 1+3*x+3*x^2 (row polynomial of A033842(2, m)).
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EXAMPLE
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{1}; {3,1}; {3,6,1}; {0,15,9,1}; {0,18,36,12,1}; ...
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CROSSREFS
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a(n, m) := s1(-2, n, m), a member of a sequence of triangles including s1(0, n, m)= A023531(n, m) (unit matrix) and s1(2, n, m)=A007318(n-1, m-1) (Pascal's triangle). s1(-1, n, m)= A030528.
Cf. A049348, A049404.
Sequence in context: A050820 A133179 A146908 this_sequence A131111 A128549 A055885
Adjacent sequences: A049321 A049322 A049323 this_sequence A049325 A049326 A049327
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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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