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A012142 Expansion of e.g.f. arctanh(arcsin(arctanh(x))), odd powers only. 1

%I

%S 1,5,137,9085,1107665,215251189,61040810841,23787478734573,

%T 12195876997744289,7959108767371738085,6442333032874852024617,

%U 6333998826435424439107165,7435387461759207059826574193,10272314131487696006461656792277,16499075087858185014891901869790713

%N Expansion of e.g.f. arctanh(arcsin(arctanh(x))), odd powers only.

%H Andrew Howroyd, <a href="/A012142/b012142.txt">Table of n, a(n) for n = 0..100</a>

%F a(n) ~ (2*n)! / (tanh(sin(1)))^(2*n+1). - _Vaclav Kotesovec_, Feb 05 2015

%e x + (5/3!)*x^3 + (137/5!)*x^5 + (9085/7!)*x^7 + ...

%p a:= n-> (t-> t!*coeff(series(arctanh(arcsin(arctanh(x))), x, t+1), x, t))(2*n+1):

%p seq(a(n), n=0..15); # _Alois P. Heinz_, Aug 17 2018

%t nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcSin[ArcTanh[x]]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* _Vaclav Kotesovec_, Feb 05 2015 *)

%o (PARI) seq(n)={my(v=Vec(serlaplace(atanh(asin(atanh(x + O(x^(2*n)))))))); vector((#v+1)\2, n, v[2*n-1])} \\ _Andrew Howroyd_, Aug 17 2018

%K nonn

%O 0,2

%A Patrick Demichel (patrick.demichel(AT)hp.com)

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Last modified January 26 16:03 EST 2022. Contains 350599 sequences. (Running on oeis4.)