A295758 O.g.f.: Sum_{n>=0} Product_{k=1..n} tan( (2*k-1)*arctan(x) ).
1, 1, 3, 15, 113, 1105, 13219, 187103, 3058113, 56675297, 1174295267, 26898243439, 674916701169, 18409502066097, 542373965958595, 17164148092886207, 580677914417571585, 20913258579319759041, 798876414332323236931, 32261582928825038942671, 1373304514339211081661169
Offset: 0
Keywords
Examples
O.g.f: A(x) = 1 + x + 3*x^2 + 15*x^3 + 113*x^4 + 1105*x^5 + 13219*x^6 + 187103*x^7 + 3058113*x^8 + 56675297*x^9 + 1174295267*x^10 + ... such that A(x) = 1 + x + x*tan(3*arctan(x)) + x*tan(3*arctan(x))*tan(5*arctan(x)) + x*tan(3*arctan(x))*tan(5*arctan(x))*tan(7*arctan(x)) + x*tan(3*arctan(x))*tan(5*arctan(x))*tan(7*arctan(x))*tan(9*arctan(x)) + ...
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..220
Programs
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PARI
{a(n)=local(X=x+x*O(x^n), Gf); Gf=sum(m=0, n, prod(k=1, m, tan((2*k-1)*atan(X)))); polcoeff(Gf, n)} for(n=0,30,print1(a(n),", "))
Formula
a(n) ~ 2^n * n^n / (exp(n) * G^(n + 1/2)), where G is the Catalan constant A006752. - Vaclav Kotesovec, Oct 02 2020