%I #16 Nov 05 2014 05:03:04
%S 1,1,4,29,384,8001,219200,7639757,338030592,18221107681,1161865470976,
%T 86954156945501,7533144553783296,744010437498030561,
%U 83107197798886031360,10418926401222040969421,1453531583873609883451392,224285068607398484964201793,38075052899686318527662522368
%N E.g.f.: Sum_{n>=0} tan(n*x)^n / n!.
%H Vaclav Kotesovec, <a href="/A210526/b210526.txt">Table of n, a(n) for n = 0..200</a>
%e E.g.f.: A(x) = 1 + x + 4*x^2/2! + 29*x^3/3! + 384*x^4/4! + 8001*x^5/5! +...
%e where
%e A(x) = 1 + tan(x) + tan(2*x)^2/2! + tan(3*x)^3/3! + tan(4*x)^4/4! + tan(5*x)^5/5! + tan(6*x)^6/6! +...
%o (PARI) {a(n)=local(X=x+x*O(x^n), Egf); Egf=sum(m=0, n, tan(m*X)^m/m!); n!*polcoeff(Egf, n)}
%o for(n=0, 20, print1(a(n), ", "))
%Y Cf. A198513, A221079.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 27 2013