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A296462 Expansion of e.g.f. arcsin(x)*arctanh(x) (even powers only). 3
0, 2, 12, 238, 9912, 708282, 77392260, 12002011110, 2507167177200, 678724656721650, 231129344455890300, 96694934804540934750, 48752132066414189721000, 29154453671147281799726250, 20403607225475633039372992500, 16520371586328834323725749873750, 15322889489994265975004588078700000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..16.

FORMULA

E.g.f.: arcsinh(x)*arctan(x) (even powers only, absolute values).

E.g.f.: i*(log(1 - x) - log(1 + x))*log(i*x + sqrt(1 - x^2))/2, where i is the imaginary unit (even powers only).

a(n) ~ Pi * (2*n-1)! / 2. - Vaclav Kotesovec, Dec 13 2017

EXAMPLE

arcsin(x)*arctanh(x) = 2*x^2/2! + 12*x^4/4! + 238*x^6/6! + 9912*x^8/8! + 708282*x^10/10! + ...

MATHEMATICA

nmax = 16; Table[(CoefficientList[Series[ArcSin[x] ArcTanh[x], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]

nmax = 16; Table[(CoefficientList[Series[I (Log[1 - x] - Log[1 + x]) Log[I x + Sqrt[1 - x^2]]/2, {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]

CROSSREFS

Cf. A001818, A009744, A009747, A010050, A012723, A296463.

Sequence in context: A309615 A166316 A011840 * A125804 A119700 A141083

Adjacent sequences:  A296459 A296460 A296461 * A296463 A296464 A296465

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 13 2017

STATUS

approved

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Last modified September 21 11:17 EDT 2020. Contains 337268 sequences. (Running on oeis4.)