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%I #11 Aug 08 2017 23:36:16
%S 1,1,1,3,3,1,16,16,6,1,125,125,50,10,1,1296,1296,540,120,15,1,16807,
%T 16807,7203,1715,245,21,1,262144,262144,114688,28672,4480,448,28,1,
%U 4782969,4782969,2125764,551124,91854,10206,756,36,1,100000000
%N Triangle of coefficients of certain polynomials (exponents in decreasing order).
%C See A049323.
%H W. Lang, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">On generalizations of Stirling number triangles</a>, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
%H Thierry Lévy, The Number of Prefixes of Minimal Factorisations of a Cycle, The Electronic Journal of Combinatorics, 23(3) (2016), #P3.35
%F a(n, m) = binomial(n+1, m)*(n+1)^(n-m-1), n >= m >= 0 else 0.
%e {1}; {1,1}; {3,3,1}; {16,16,6,1}; {125,125,50,10,1}; .... E.g. third row {3,3,1} corresponds to polynomial p(2,x)= 3*x^2+3*x+1.
%Y a(n, 0)= A000272(n+1), n >= 0 (first column), a(n, 1)= A000272(n+1), n >= 1 (second column). p(k-1, -x)/(1-k*x)^k = (-1+1/(1-k*x)^k)/(x*k^2) is for k=1..5 G.f. for A000012, A001792, A036068, A036070, A036083, respectively.
%Y See also A049323.
%K easy,nonn,tabl
%O 0,4
%A _Wolfdieter Lang_
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