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%I #10 Aug 09 2024 05:17:33
%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 Triangle begins:
%e {1};
%e {2,1};
%e {5,5,1};
%e {30,30,10,1};
%e {272,272,102,17,1};
%e ....
%e 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_