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E.g.f. 1/(1 - tan(2*x))^(1/2).
3

%I #9 Sep 23 2022 17:03:56

%S 1,1,3,23,201,2401,33723,564983,10832721,235620481,5715989043,

%T 153231400343,4495861836441,143343873560161,4934418832685163,

%U 182409363179578103,7206898465033427361,303073359560984509441,13516205633151976330083,637174194752117499594263

%N E.g.f. 1/(1 - tan(2*x))^(1/2).

%C Generally, for e.g.f. 1/(1-tan(p*x))^(1/p) is a(n) ~ n! * 2^(2*n+1/p) * p^n / (Gamma(1/p) * Pi^(n+1/p) * n^(1-1/p)).

%F a(n) ~ n! * 2^(3*n+1/2) / (Pi^(n+1) * sqrt(n)).

%t CoefficientList[Series[1/(1 - Tan[2*x])^(1/2), {x, 0, 20}], x] * Range[0, 20]!

%Y Cf. A000828 (p=1), A235132 (p=3).

%K nonn,easy

%O 0,3

%A _Vaclav Kotesovec_, Jan 03 2014