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 A012142 Expansion of e.g.f. arctanh(arcsin(arctanh(x))), odd powers only. 1
 1, 5, 137, 9085, 1107665, 215251189, 61040810841, 23787478734573, 12195876997744289, 7959108767371738085, 6442333032874852024617, 6333998826435424439107165, 7435387461759207059826574193, 10272314131487696006461656792277, 16499075087858185014891901869790713 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..100 FORMULA a(n) ~ (2*n)! / (tanh(sin(1)))^(2*n+1). - Vaclav Kotesovec, Feb 05 2015 EXAMPLE x + (5/3!)*x^3 + (137/5!)*x^5 + (9085/7!)*x^7 + ... MAPLE a:= n-> (t-> t!*coeff(series(arctanh(arcsin(arctanh(x))), x, t+1), x, t))(2*n+1): seq(a(n), n=0..15);  # Alois P. Heinz, Aug 17 2018 MATHEMATICA 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 *) PROG (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 CROSSREFS Sequence in context: A159546 A339566 A012215 * A012207 A192640 A192641 Adjacent sequences:  A012139 A012140 A012141 * A012143 A012144 A012145 KEYWORD nonn AUTHOR Patrick Demichel (patrick.demichel(AT)hp.com) STATUS approved

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Last modified November 29 01:40 EST 2021. Contains 349416 sequences. (Running on oeis4.)