A059341 Triangle giving numerators of coefficients of Euler polynomials, highest powers first.
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, 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, -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
Offset: 0
Examples
1; x-1/2; x^2-x; x^3-3*x^2/2+1/4; ...
References
- 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.
- L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 48, [14b].
Links
- G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
- M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Crossrefs
Programs
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Maple
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:
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Mathematica
Numerator[Table[Reverse[CoefficientList[Series[EulerE[n, x], {x, 0, 20}], x]], {n, 0, 10}]]//Flatten (* G. C. Greubel, Jan 07 2017 *)
Extensions
More terms from James Sellers, Jan 29 2001