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Expansion of e.g.f. sinh(log(1+tan(x))).
2

%I #17 Jan 22 2018 02:39:16

%S 0,1,-1,5,-20,136,-976,8840,-88640,1019776,-12933376,181318400,

%T -2767631360,45821372416,-816582578176,15596531778560,

%U -317710534983680,6876972491309056,-157606194409701376,3812752893951672320,-97090584769337753600,2596013487025352605696

%N Expansion of e.g.f. sinh(log(1+tan(x))).

%H G. C. Greubel, <a href="/A009569/b009569.txt">Table of n, a(n) for n = 0..430</a>

%F a(n) ~ n! * (-1)^(n+1) * 4^n / Pi^(n+1). - _Vaclav Kotesovec_, Jan 23 2015

%t CoefficientList[Series[(Tan[x]*(2 + Tan[x]))/(2*(1 + Tan[x])), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 23 2015 *)

%t With[{nmax = 50}, CoefficientList[Series[Sinh[Log[1 + Tan[x]]], {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Jan 21 2018 *)

%o (PARI) x='x+O('x^30); concat([0], Vec(serlaplace(sinh(log(1+tan(x)))))) \\ _G. C. Greubel_, Jan 21 2018

%K sign,easy

%O 0,4

%A _R. H. Hardin_

%E Extended with signs by _Olivier GĂ©rard_, Mar 15 1997

%E Terms a(20) and a(21) added by _G. C. Greubel_, Jan 21 2018