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A012262
Expansion of e.g.f. exp(arctanh(arcsinh(x))).
1
1, 1, 1, 2, 5, 24, 109, 552, 3177, 28032, 227961, 1778688, 15773229, 212383872, 2521786149, 25215328512, 294715261521, 5734229114880, 91106569198449, 1029078328135680, 14283819393505749, 410202091438571520
OFFSET
0,4
COMMENTS
a(32) is negative. - Vaclav Kotesovec, Oct 25 2013
LINKS
FORMULA
a(n) ~ 8*n^(n-1)*(2*sin(Pi*n/2)-Pi*cos(Pi*n/2))/((4+Pi^2)^(3/2)*exp(n)). - Vaclav Kotesovec, Oct 25 2013
EXAMPLE
E.g.f. = 1 + x + x^2/2! + 2*x^3/3! + 5*x^4/4! + 24*x^5/5! + ...
MAPLE
seq(coeff(series(factorial(n)*exp(arctanh(arcsinh(x))), x, n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Oct 29 2018
MATHEMATICA
CoefficientList[Series[Exp[ArcTanh[ArcSinh[x]]], {x, 0, 35}], x]* Range[0, 35]! (* Vaclav Kotesovec, Oct 25 2013 *)
PROG
(PARI) x='x+O('x^30); Vec(serlaplace(exp(atanh(asinh(x))))) \\ G. C. Greubel, Oct 28 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(Argtanh(Argsinh(x))) )); [Factorial(n-1)*b[n]: n in [1..m-1]]; // G. C. Greubel, Oct 28 2018
CROSSREFS
Sequence in context: A200402 A010365 A218939 * A012254 A322897 A284230
KEYWORD
sign
AUTHOR
Patrick Demichel (patrick.demichel(AT)hp.com)
STATUS
approved