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A051187 Generalized Stirling number triangle of first kind. 4
1, -8, 1, 128, -24, 1, -3072, 704, -48, 1, 98304, -25600, 2240, -80, 1, -3932160, 1122304, -115200, 5440, -120, 1, 188743680, -57802752, 6651904, -376320, 11200, -168, 1, -10569646080, 3425697792, -430309376, 27725824, -1003520, 20608, -224, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n,m)= R_n^m(a=0,b=8) 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-8*j,j=0..n-1), n >= 1, E(0,x) := 1, are exponential convolution polynomials (see A039692 for the definition and a Knuth reference).

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.

LINKS

Table of n, a(n) for n=1..36.

FORMULA

a(n, m) = a(n-1, m-1) - 8*(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: (((log(1+8*x))/8)^m)/m!.

EXAMPLE

{1}; {-8,1}; {128,-24,1}; {-3072,704,-48,1}; ... E(3,x) = 128*x-24*x^2+x^3.

CROSSREFS

First (m=1) column sequence is: A051189(n-1). Row sums (signed triangle): A049210(n-1)*(-1)^(n-1). Row sums (unsigned triangle): A045755(n). The b=1..7 triangles are: A008275 (Stirling1 triangle), A039683, A051141, A051142, A051150, A051151, A051186.

Sequence in context: A048786 A240955 A132056 * A284865 A221758 A322699

Adjacent sequences:  A051184 A051185 A051186 * A051188 A051189 A051190

KEYWORD

sign,easy,tabl

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified January 16 23:44 EST 2019. Contains 319206 sequences. (Running on oeis4.)