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Search: id:A049326
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| A049326 |
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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, 10, 1, 50, 20, 1, 125, 200, 30, 1, 125, 1250, 450, 40, 1, 0, 5250, 4375, 800, 50, 1, 0, 15000, 30375, 10500, 1250, 60, 1, 0, 28125, 157500, 100500, 20625, 1800, 70, 1, 0, 31250, 621875, 740000, 250625, 35750, 2450, 80, 1, 0, 15625, 1875000, 4318750
(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) = 5*(5*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(4, x))^m, p(4, x) := 1+10*x+50*x^2+125*x^3+125*x^4 (row polynomial of A033842(4, m)).
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EXAMPLE
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{1}; {10,1}; {50,20,1}; {125,200,30,1}; {125,1250,450,40,1}; ...
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CROSSREFS
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a(n, m) := s1(-4, 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. A049350.
Sequence in context: A115097 A050313 A116574 this_sequence A146537 A050304 A143471
Adjacent sequences: A049323 A049324 A049325 this_sequence A049327 A049328 A049329
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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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