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A048176
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Generalized Stirling number triangle of first kind.
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3
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1, -10, 1, 200, -30, 1, -6000, 1100, -60, 1, 240000, -50000, 3500, -100, 1, -12000000, 2740000, -225000, 8500, -150, 1, 720000000, -176400000, 16240000, -735000, 17500, -210, 1, -50400000000, 13068000000, -1313200000, 67690000, -1960000, 32200, -280, 1, 4032000000000, -1095840000000
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n,m)= R_n^m(a=0,b=10) in the notation of the given reference.
a(n,m) is a Jabotinsky matrix, i.e. the monic row polynomials E(n,x) := sum(a(n,m)*x^m,m=1..n) = product(x-10*j,j=0..n-1), n >= 1, E(0,x) := 1, are exponential convolution polynomials (see A039692 for the definition and a Knuth reference).
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REFERENCES
| Mitrinovic, D. S.; Mitrinovic, R. S.; Tableaux d'une classe de nombres relies aux nombres de Stirling. Univ. Beograd. Pubi. Elektrotehn. Fak. Ser. Mat. Fiz. No. 77 1962, 77 pp.
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FORMULA
| a(n, m) = a(n-1, m-1) - 10*(n-1)*a(n-1, m), n >= m >= 1; a(n, m) := 0, n<m; a(n, 0) := 0, a(1, 1)=1. E.g.f. for m-th column of signed triangle: (((ln(1+10*x))/10)^m)/m!.
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EXAMPLE
| {1}; {-10,1}; {200,-30,1}; {-6000,1100,-60,1}; ... E(3,x) = 200*x-30*x^2+x^3.
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CROSSREFS
| First (m=1) (unsigned) column sequence is: A051262(n-1). Row sums (signed triangle): A049212(n-1)*(-1)^(n-1). Row sums (unsigned triangle): A045757(n). b=8: A051187, b=9: A051231.
Sequence in context: A156286 A049223 A131367 * A127616 A191549 A071938
Adjacent sequences: A048173 A048174 A048175 * A048177 A048178 A048179
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KEYWORD
| sign,easy,tabl
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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