|
%I #9 Apr 10 2013 12:48:11
%S 1,1,-1,-1,1,-2,-5,6,4,1,-3,-12,29,57,-72,-46,1,-4,-22,80,261,-660,
%T -1264,1608,1024,1,-5,-35,170,775,-2941,-9385,23880,45620,-58080,
%U -36976,1,-6,-51,310,1815,-9186,-41033,156618,498660,-1269720,-2425056,3087648
%N Triangle read by rows, coefficients of the Swiss-Knife median polynomials M_{n}(x) in descending order of powers.
%C M(n,0) = M(n,1) = A099023(n) = (-1)^n*A000657(n).
%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform.</a>
%e M(0,x) = 1,
%e M(1,x) = x^2-x-1,
%e M(2,x) = x^4-2*x^3-5*x^2+6*x+4,
%e M(3,x) = x^6-3*x^5-12*x^4+29*x^3+57*x^2-72*x-46.
%p A213736_triangle := proc(n) local A, len, k, m, sk_poly;
%p len := 2*n-1; A := array(0..len,0..len);
%p sk_poly := proc(n, x) local v, k;
%p add(`if`((k+1)mod 4 = 0,0,(-1)^iquo(k+1,4))*2^iquo(-k,2)*
%p add((-1)^v*binomial(k,v)*(v+x+1)^n,v=0..k),k=0..n) end:
%p for m from 0 to len do A[m,0] := sk_poly(m,x);
%p for k from m-1 by -1 to 0 do
%p A[k,m-k] := A[k+1,m-k-1] - A[k,m-k-1] od od;
%p seq(print(seq(coeff(A[k,k],x,2*k-i),i=0..2*k)),k=0..n-1) end:
%p A213736_triangle(5);
%Y Cf. A153641, A162660.
%K sign,tabf
%O 0,6
%A _Peter Luschny_, Jun 19 2012
|
