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Search: id:A049327
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| A049327 |
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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, 15, 1, 120, 30, 1, 540, 465, 45, 1, 1296, 4680, 1035, 60, 1, 1296, 33192, 15795, 1830, 75, 1, 0, 171072, 176688, 37260, 2850, 90, 1, 0, 641520, 1521828, 563409, 72450, 4095, 105, 1, 0, 1710720, 10359360, 6686064, 1375605, 124740, 5565, 120, 1
(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) = 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: (x*p(5, x))^m, p(5, x) := 1+15*x+120*x^2+540*x^3+1296*x^4+1296*x^5 (row polynomial of A033842(5, m)).
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EXAMPLE
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{1}; {15,1}; {120,30,1}; {540,465,45,1}; {1296,4680,1035,60,1}; ...
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CROSSREFS
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a(n, m) := s1(-5, 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. A049351.
Sequence in context: A040239 A126141 A131514 this_sequence A030527 A027467 A049375
Adjacent sequences: A049324 A049325 A049326 this_sequence A049328 A049329 A049330
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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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