Search: id:A049323
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%I A049323
%S A049323 1,1,1,1,3,3,1,6,16,16,1,10,50,125,125,1,15,120,540,1296,1296,1,21,245,
%T A049323 1715,7203,16807,16807,1,28,448,4480,28672,114688,262144,262144,1,36,
%U A049323 756,10206,91854,551124,2125764,4782969,4782969,1,45,1200,21000,252000
%N A049323 Triangle of coefficients of certain polynomials (exponents in increasing 
               order), equivalent to A033842.
%H A049323 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.
%F A049323 a(n, m) = A033842(n, n-m) = binomial(n+1, m+1)*(n+1)^{m-1}, n >= m >= 
               0, else 0.
%F A049323 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.
%e A049323 {1}; {1,1}; {1,3,3}; {1,6,16,16}; {1,10,50,125,125}; .... E.g. third 
               row {1,3,3} corresponds to polynomial p{3,x)= 1+3*x+3*x^2.
%Y A049323 a(n, 0)= A000012 (powers of 1), a(n, 1)= A000217 (triangular numbers), 
               a(n, n)= A000272(n+1), n >= 0 (diagonal), a(n, n-1)= A000272(n+1), 
               n >= 1.
%Y A049323 For n = 0..5 the row sequences a(n, m), m >= 0, are the first columns 
               of the triangles A023531 (unit matrix), A030528, A049324, A049325, 
               A049326, A049327, respectively.
%Y A049323 Cf. A033842, A046757.
%Y A049323 Sequence in context: A001498 A138464 A117279 this_sequence A084144 A116401 
               A106479
%Y A049323 Adjacent sequences: A049320 A049321 A049322 this_sequence A049324 A049325 
               A049326
%K A049323 easy,nonn,tabl
%O A049323 0,5
%A A049323 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)

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