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%I #9 May 21 2013 08:49:53
%S 1,2,-1,1,-1,0,4,-6,0,1,1,-2,0,1,0,2,-5,0,5,0,-1,1,-3,0,5,0,-3,0,8,
%T -28,0,70,0,-84,0,17,1,-4,0,14,0,-28,0,17,0,2,-9,0,42,0,-126,0,153,0,
%U -31,1,-5,0,30,0,-126,0,255,0,-155,0,4,-22,0,165,0,-924
%N Triangle read by rows, coefficients of the Euler polynomials E_{n}(x) times A006519(n+1) in descending order of powers.
%e e(0,x) = 1,
%e e(1,x) = 2*x^1 - 1,
%e e(2,x) = x^2 - x^1,
%e e(3,x) = 4*x^3 - 6*x^2 + 1,
%e e(4,x) = x^4 - 2*x^3 + x^1,
%e e(5,x) = 2*x^5 - 5*x^4 + 5*x^2 - 1.
%p seq(seq(coeff(2^padic[ordp](i+1,2)*euler(i,x),x,i-j),j=0..i),i=0..11);
%t Table[ CoefficientList[ EulerE[n, x]*2^IntegerExponent[n+1, 2], x] // Reverse, {n, 0, 11}] // Flatten (* _Jean-François Alcover_, May 21 2013 *)
%K sign,tabl
%O 0,2
%A _Peter Luschny_, Jun 16 2012
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