1,2

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).

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.

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: (((ln(1+8*x))/8)^m)/m!.

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

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: A114152 A048786 A132056 this_sequence A021850 A011105 A098829

Adjacent sequences: A051184 A051185 A051186 this_sequence A051188 A051189 A051190

sign,easy,tabl

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)