A221080 E.g.f.: Sum_{n>=0} Product_{k=1..n} tan((2*k-1)*x).
1, 1, 6, 92, 2760, 134416, 9626976, 952336832, 124374587520, 20725471027456, 4290994105591296, 1080503158073449472, 325167279095248865280, 115252343303110680580096, 47519237579074974018134016, 22549702636577116941673152512, 12202485589681663721911088087040
Offset: 0
Keywords
Examples
E.g.f.: A(x) = 1 + x + 6*x^2/2! + 92*x^3/3! + 2760*x^4/4! + 134416*x^5/5! +... where A(x) = 1 + tan(x) + tan(x)*tan(3*x) + tan(x)*tan(3*x)*tan(5*x) + tan(x)*tan(3*x)*tan(5*x)*tan(7*x) + tan(x)*tan(3*x)*tan(5*x)*tan(7*x)*tan(9*x) +...
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..150
Programs
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PARI
{a(n)=local(X=x+x*O(x^n), Egf); Egf=sum(m=0, n, prod(k=1, m, tan((2*k-1)*X))); n!*polcoeff(Egf, n)} for(n=0, 20, print1(a(n), ", "))
Formula
a(n) ~ sqrt(Pi) * 2^(n+1/2) * n^(2*n+1/2) / (exp(2*n) * G^(n+1/2)), where G = A006752 = 0.915965594177219... is Catalan's constant. - Vaclav Kotesovec, Nov 02 2014