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

0,8

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].

Example

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

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:

Mathematica

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

Crossrefs

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

Sequence in context: A181872 A239264 A294289 * A249442 A334739 A131802

Adjacent sequences: A059338 A059339 A059340 * A059342 A059343 A059344

Keyword

sign,tabf,frac,easy

Author

N. J. A. Sloane, Jan 27 2001

Extensions

More terms from James A. Sellers, Jan 29 2001

Status

approved