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Search: id:A049325
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| A049325 |
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A convolution triangle of numbers generalizing Pascal's triangle A007318. |
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+0
4
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| 1, 6, 1, 16, 12, 1, 16, 68, 18, 1, 0, 224, 156, 24, 1, 0, 448, 840, 280, 30, 1, 0, 512, 3072, 2080, 440, 36, 1, 0, 256, 7872, 10896, 4160, 636, 42, 1, 0, 0, 14080, 42240, 28240, 7296, 868, 48, 1, 0, 0, 16896, 123904, 145376, 60720, 11704, 1136, 54, 1, 0, 0, 12288
(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) = 4*(4*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(3, x))^m, p(3, x) := 1+6*x+16*x^2+16*x^3 (row polynomial of A033842(3, m)).
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EXAMPLE
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{1}; {6,1}; {16,12,1}; {16,68,18,1}; {0,224,156,24,1}; ...
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CROSSREFS
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a(n, m) := s1(-3, 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, s1(-2, n, m)= A049324(n, m).
Cf. A049349.
Sequence in context: A136273 A125233 A139727 this_sequence A092371 A157386 A157396
Adjacent sequences: A049322 A049323 A049324 this_sequence A049326 A049327 A049328
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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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