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A046757 Triangle of coefficients of certain polynomials (exponents in decreasing order). 1

%I #4 Mar 31 2012 13:19:58

%S 1,2,1,5,5,1,30,30,10,1,272,272,102,17,1,3250,3250,1300,260,26,1,

%T 47952,47952,19980,4440,555,37,1,840350,840350,360150,85750,12250,

%U 1050,50,1,17039360,17039360,7454720,1863680,291200,29120,1820,65,1,392203458

%N Triangle of coefficients of certain polynomials (exponents in decreasing order).

%F a(n, n)= 1, a(n, m)= (1+n^2)*binomial(n, m)*n^(n-m-2), n>m >= 0, else 0.

%e {1}; {2,1}; {5,5,1}; {30,30,10,1}; {272,272,102,17,1}; .... E.g. third row {5,5,1} corresponds to polynomial q{3,x)= 5*x^2+5*x+1.

%Y x*p(k-1, -x)/q(k, -x), with the row polynomials p(n, x) from triangle A033842(n, m) is for k=1..5 G.f. for A000079 (powers of two), A039717, A043553, A045624, A046088, respectively.

%K easy,nonn,tabl

%O 0,2

%A _Wolfdieter Lang_

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