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

1,3

Links

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

Formula

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

Prog

(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
(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

Crossrefs

Cf. A002430, A046990, A130654.

Sequence in context: A246600 A068068 A193523 * A066086 A323406 A160520

Adjacent sequences: A092502 A092503 A092504 * A092506 A092507 A092508

Keyword

nonn

Author

Ralf Stephan, Apr 05 2004

Status

approved