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Triangle giving numerators of coefficients of Euler polynomials, highest powers first.
2

%I #15 May 08 2018 15:11:55

%S 1,1,-1,1,-1,0,1,-3,0,1,1,-2,0,1,0,1,-5,0,5,0,-1,1,-3,0,5,0,-3,0,1,-7,

%T 0,35,0,-21,0,17,1,-4,0,14,0,-28,0,17,0,1,-9,0,21,0,-63,0,153,0,-31,1,

%U -5,0,30,0,-126,0,255,0,-155,0,1,-11,0,165,0,-231,0,2805,0,-1705,0,691,1,-6,0,55,0,-396,0,1683,0,-3410,0,2073,0,1,-13

%N Triangle giving numerators of coefficients of Euler polynomials, highest powers first.

%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 809.

%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 48, [14b].

%H G. C. Greubel, <a href="/A059341/b059341.txt">Table of n, a(n) for the first 50 rows, flattened</a>

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

%e 1; x-1/2; x^2-x; x^3-3*x^2/2+1/4; ...

%p for n from 0 to 30 do for k from n to 0 by -1 do printf(`%d,`,numer(coeff(euler(n,x), x, k))) od:od:

%t Numerator[Table[Reverse[CoefficientList[Series[EulerE[n, x], {x, 0, 20}], x]], {n, 0, 10}]]//Flatten (* _G. C. Greubel_, Jan 07 2017 *)

%Y Cf. A059342. See also A004172, A004173, A004174, A004175, A011934, A020523, A020524, A020525, A020526, A020547, A020548, A058940.

%K sign,tabf,frac,easy

%O 0,8

%A _N. J. A. Sloane_, Jan 27 2001

%E More terms from _James A. Sellers_, Jan 29 2001