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Search: id:A075505
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| A075505 |
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Stirling2 triangle with scaled diagonals (powers of 10). |
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+0
3
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| 1, 10, 1, 100, 30, 1, 1000, 700, 60, 1, 10000, 15000, 2500, 100, 1, 100000, 310000, 90000, 6500, 150, 1, 1000000, 6300000, 3010000, 350000, 14000, 210, 1, 10000000, 127000000, 96600000, 17010000, 1050000
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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This is a lower triangular infinite matrix of the Jabotinsky type. See the Knuth reference given in A039692 for exponential convolution arrays.
The row polynomials p(n,x) := sum(a(n,m)x^m,m=1..n), n>=1, have e.g.f. J(x; z)= exp((exp(10*z)-1)*x/10)-1.
Row sums give A075509(n),n>=1.
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FORMULA
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a(n, m)=(10^(n-m))S2(n, m) with S2(n, m) := A008277(n, m) (Stirling2).
a(n, m)=sum((A075513(m, p)*((p+1)*10)^(n-m))/(m-1)!, p=0..m-1) for n>=m>=1 else 0.
a(n, m)=10m*a(n-1, m) + a(n-1, m-1), n>=m>=1, else 0, with a(n, 0) := 0 and a(1, 1)=1.
G.f. for m-th column: (x^m)/product(1-10k*x, k=1..m), m>=1.
E.g.f. for m-th column: (((exp(10x)-1)/10)^m)/m!, m>=1.
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EXAMPLE
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[1]; [10,1]; [100,30,1]; ...; p(3,x)=x(100+30*x+x^2).
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CROSSREFS
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Cf. A075504.
Sequence in context: A164881 A165293 A038303 this_sequence A130310 A051523 A048882
Adjacent sequences: A075502 A075503 A075504 this_sequence A075506 A075507 A075508
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 02, 2002
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