cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A279370 Numerators of coefficients in expansion of (cos(sqrt(x)))/(1 + cos(sqrt(x))).

Original entry on oeis.org

1, -1, -1, -17, -31, -691, -5461, -929569, -3202291, -221930581, -4722116521, -56963745931, -14717667114151, -2093660879252671, -86125672563201181, -129848163681107301953, -868320396104950823611, -209390615747646519456961, -14129659550745551130667441
Offset: 0

Views

Author

Clark Kimberling, Dec 12 2016

Keywords

Comments

Differs from A089171 in signs; see Formula.

Examples

			(1/2) - (1/8)x - (1/48)x^2 - (17/5760)x^3 + ... ; 1/2, - 1/8, - 48/2, - 17/5760, ... = A279370/A279109.
		

Crossrefs

Programs

  • Mathematica
    z = 26; t = CoefficientList[Series[Cos[Sqrt[x]]/(1 + Cos[Sqrt[x]]), {x, 0, z}], x];
    Numerator[t]   (* A279370 *)
    Denominator[t] (* A279109 *)

Formula

For odd n and for n = 0, we have a(n) = A089171(n); for positive even n, however, a(n) = -A089171(n)

A279110 Denominators of coefficients in expansion of 2/(1 + cos(sqrt(x))).

Original entry on oeis.org

1, 4, 24, 2880, 40320, 7257600, 479001600, 697426329600, 20922789888000, 12804747411456000, 2432902008176640000, 264470759477084160000, 620448401733239439360000, 806582922253211271168000000, 304888344611713860501504000000, 4244045756995056938180935680000000
Offset: 0

Views

Author

Clark Kimberling, Dec 07 2016

Keywords

Examples

			1/1 + (1/4)x + (1/24)x^2 + (17/2880)x^3 + ... ; 1/1, 1/4, 1/24, 17/2880, 31/40320, ... = |A089171|/A279110.
		

Crossrefs

Programs

  • Mathematica
    z = 26; t = CoefficientList[Series[2/(1 + Cos[Sqrt[x]]), {x, 0, z}], x];
    Numerator[t]   (* A089171, unsigned *)
    Denominator[t] (* A279110 *)

Formula

Showing 1-2 of 2 results.