A089626 - OEIS

%I #9 Oct 16 2015 16:56:07

%S 1,45,4465125,6272287562165625,438120013555654794702228515625,

%T 3943988517696329309474874414036059896739501953125,

%U 9860368980530253649041813027973243717504383071655695011832599639892578125

%N a(n) = 1/h(n) where {h(n)} is the Hankel transform of {t(n)}; t(n) is defined by the expansion of tan(x)= Sum_n>0, t(n)*x^(2*n-1); |x|<Pi/2.

%C t(n)= (2^(2*n)-1)*2^(2*n)*B_n /(2*n)! B_n: numbers of Bernoulli, sequence 1/6, 1/30, 1/42, 1/30, 5/66, ... example:n=2, a(2)= 1/det|1, 1/3|1/3, 2/15|= 1/(1/45)=45 See A001906 for the definition of Hankel transform.

%F a(n) = (4*n-3)^1*(4*n-5)^2*...*3^(2*n-2)*1^(2*n-1).

%F a(n) = A057863(2*n-1). - _Vaclav Kotesovec_, Oct 16 2015

%Y Cf. A057863.

%K easy,nonn

%O 1,2

%A _Philippe Deléham_, Dec 31 2003