A092505 - OEIS

%I #16 Aug 26 2024 05:02:43

%S 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,

%T 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,

%U 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

%N a(n) = A002430(n) / A046990(n).

%H Antti Karttunen, <a href="/A092505/b092505.txt">Table of n, a(n) for n = 1..16385</a>

%F A007814(a(n)) = A130654(n). - _Antti Karttunen_, Jan 12 2019

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

%o (PARI)

%o \\ Quite wasteful, especially as there is the same bernfrac(2*n) in both. Should reduce to a much simpler form?

%o 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.

%o A046990(n) = numerator(((-4)^n-(-16)^n)*bernfrac(2*n)/2/n/(2*n)!); \\ From A046990

%o A092505(n) = (A002430(n) / A046990(n)); \\ _Antti Karttunen_, Jan 12 2019

%o (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

%Y Cf. A002430, A046990, A130654.

%K nonn

%O 1,3

%A _Ralf Stephan_, Apr 05 2004