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A030527
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A convolution triangle of numbers obtained from A036083.
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4
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1, 15, 1, 175, 30, 1, 1750, 575, 45, 1, 15750, 8750, 1200, 60, 1, 131250, 114625, 24375, 2050, 75, 1, 1031250, 1347500, 414750, 52000, 3125, 90, 1, 7734375, 14575000, 6208125, 1084875, 95000, 4425, 105, 1, 55859375, 147468750, 84184375
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OFFSET
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1,2
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COMMENTS
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a(n,m) := s1p(6; 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(6; n,m).
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LINKS
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Table of n, a(n) for n=1..39.
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*(1-10*x+50*x^2-125*x^3+125*x^4)/(1-5*x)^5)^m.
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EXAMPLE
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{1}; {15,1}; {175,30,1}; {1750,575,45,1}; {15750,8750,1200,60,1}; ...
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CROSSREFS
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a(n, 1)= A036083(n-1). Row sums = A046088(n).
Sequence in context: A126141 A131514 A049327 * A027467 A049375 A049224
Adjacent sequences: A030524 A030525 A030526 * A030528 A030529 A030530
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Wolfdieter Lang
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STATUS
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approved
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