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A296439 Expansion of e.g.f. log(1 + arctanh(x))*exp(x). 5
0, 1, 1, 4, 0, 53, -155, 2364, -15288, 216817, -2147215, 32932700, -433435816, 7431919285, -120703007451, 2326504612964, -44614898438480, 963118686971137, -21195404220321151, 508991484878443860, -12604990423335824688, 334199905021923072597, -9181752759370241656699, 266806716890671639953964 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
E.g.f.: log(1 + (log(1 + x) - log(1 - x))/2)*exp(x).
a(n) ~ -(-1)^n * (n-1)! * exp((1-exp(2))/(1+exp(2))) * ((exp(2)+1)/(exp(2)-1))^n. - Vaclav Kotesovec, Dec 21 2017
EXAMPLE
E.g.f.: A(x) = x/1! + x^2/2! + 4*x^3/3! + 53*x^5/5! - 155*x^6/6! + 2364*x^7/7! - 15288*x^8/8! + ...
MAPLE
a:=series(log(1+arctanh(x))*exp(x), x=0, 24): seq(n!*coeff(a, x, n), n=0..23); # Paolo P. Lava, Mar 27 2019
MATHEMATICA
nmax = 23; CoefficientList[Series[Log[1 + ArcTanh[x]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 23; CoefficientList[Series[Log[1 + (Log[1 + x] - Log[1 - x])/2] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
PROG
(PARI) my(ox=O(x^30)); Vecrev(Pol(serlaplace(log(1 + atanh(x + ox)) * exp(x + ox)))) \\ Andrew Howroyd, Dec 12 2017
CROSSREFS
Sequence in context: A101502 A118440 A247119 * A228557 A358294 A298616
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Dec 12 2017
STATUS
approved

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Last modified February 24 22:04 EST 2024. Contains 370307 sequences. (Running on oeis4.)