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A058940 Triangle of coefficients of Euler polynomials rescaled to integers by multiplication with 2^(binary carry sequence (A007814)).

%I A058940 #17 Jul 12 2019 09:08:04
%S A058940 1,-1,2,0,-1,1,1,0,-6,4,0,1,0,-2,1,-1,0,5,0,-5,2,0,-3,0,5,0,-3,1,17,0,
%T A058940 -84,0,70,0,-28,8,0,17,0,-28,0,14,0,-4,1,-31,0,153,0,-126,0,42,0,-9,2,
%U A058940 0,-155,0,255,0,-126,0,30,0,-5,1,691,0,-3410,0,2805,0,-924,0,165,0,-22,4,0,2073,0,-3410,0,1683,0,-396,0,55,0,-6
%N A058940 Triangle of coefficients of Euler polynomials rescaled to integers by multiplication with 2^(binary carry sequence (A007814)).
%C A058940 Sums of even rows are A002425, sums of odd rows are 0, first element of even rows is -row sum, first element of row(2^p) is second element of row(1+2^p), LCM of numerators of Euler polynomial coefficients is A007814.
%F A058940 T(n, k) = [x^k] E(n, x)*2^A007814(n+1).
%p A058940 A058940_row := proc(n) local i; seq(coeff(euler(n,x)*2^padic[ordp](n+1,2),x,i), i=0..n) end: # _Peter Luschny_, Nov 26 2010
%t A058940 Flatten[ Table[ CoefficientList[ EulerE[n, x]*2^IntegerExponent[n+1, 2], x], {n, 0, 12}]] (* _Jean-François Alcover_, Nov 18 2011, after _Wouter Meeussen_ *)
%Y A058940 Cf. A004174, A002425, A007814.
%K A058940 tabl,nice,sign
%O A058940 0,3
%A A058940 _Wouter Meeussen_, Jan 12 2001