A092505 a(n) = A002430(n) / A046990(n).

1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 4, 2, 1, 2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4, 2, 1, 2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 8, 2, 4, 2, 1, 2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 8, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4

Offset: 1

Author

Ralf Stephan, Apr 05 2004

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16385

Crossrefs

Cf. A002430, A046990, A130654.

Programs

Magma

[Numerator((-1)^(n - 1)*2^(2*n)*(2^(2*n) - 1)*Bernoulli(2*n) / Factorial(2*n)) / (Numerator(((-4)^n-(-16)^n) * Bernoulli(2*n) / 2 / n / Factorial(2*n))): n in [1..100]]; // Vincenzo Librandi, Jan 13 2019

PARI

a(n)=if(n<1,0,numerator(polcoeff(Ser(tan(x)),2*n-1))/numerator(polcoeff(Ser(log(1/cos(x))),2*n)))

PARI

\\ Quite wasteful, especially as there is the same bernfrac(2*n) in both. Should reduce to a much simpler form?
A002430(n) = numerator(((-1)^(n-1)) * 2^(2*n) * (2^(2*n)-1)*bernfrac(2*n)/((2*n)!)); \\ After Johannes W. Meijer's May 24 2009 formula in A002430.
A046990(n) = numerator(((-4)^n-(-16)^n)*bernfrac(2*n)/2/n/(2*n)!); \\ From A046990
A092505(n) = (A002430(n) / A046990(n)); \\ Antti Karttunen, Jan 12 2019

Formula

A007814(a(n)) = A130654(n). - Antti Karttunen, Jan 12 2019