A059342 Triangle giving denominators of coefficients of Euler polynomials, highest powers first.
1, 1, 2, 1, 1, 1, 1, 2, 1, 4, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 4, 1, 2, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 4, 1, 1, 1, 4, 1, 2, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2
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,`,denom(coeff(euler(n,x), x, k))) od:od:
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Mathematica
Denominator[Table[Reverse[CoefficientList[Series[EulerE[n, x], {x, 0, 20}], x]], {n, 0, 10}]] (* G. C. Greubel, Jan 07 2017 *)
Extensions
More terms from James Sellers, Jan 29 2001