A296622 - OEIS

A296622

Expansion of e.g.f. log(1 + arcsin(x)*arcsinh(x)) (even powers only).

0, 2, -12, 328, -15008, 1356192, -166628352, 31500831360, -7474571071488, 2418220114014720, -940432709166170112, 464609611973533501440, -268355615175956213268480, 188067307050238642631516160, -151072053399934628129585233920, 142618740583722182161589570273280

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..15.

FORMULA

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

EXAMPLE

log(1 + arcsin(x)*arcsinh(x)) = 2*x^2/2! - 12*x^4/4! + 328*x^6/6! - 15008*x^8/8! + 1356192*x^10/10! - 166628352*x^12/12! + ...

MATHEMATICA

nmax = 15; Table[(CoefficientList[Series[Log[1 + ArcSin[x] ArcSinh[x]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]

nmax = 15; Table[(CoefficientList[Series[Log[1 - I Log[I x + Sqrt[1 - x^2]] Log[x + Sqrt[1 + x^2]]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]

CROSSREFS

Cf. A001818, A009232, A009359, A012598, A189815, A296435.

Sequence in context: A091472 A156518 A012727 * A325756 A181142 A088229

Adjacent sequences: A296619 A296620 A296621 * A296623 A296624 A296625

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Dec 17 2017

STATUS

approved