A296727 - OEIS

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A296727

Expansion of e.g.f. arcsinh(x)/(1 - x).

0, 1, 2, 5, 20, 109, 654, 4353, 34824, 324441, 3244410, 34795485, 417545820, 5536151685, 77506123590, 1144330385625, 18309286170000, 315366695240625, 5676600514331250, 106667957800963125, 2133359156019262500, 45229212438054868125, 995042673637207098750, 22696937952367956440625

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..23.

FORMULA

E.g.f.: log(x + sqrt(1 + x^2))/(1 - x).

a(n) ~ n! * log(1 + sqrt(2)). - Vaclav Kotesovec, Dec 20 2017

EXAMPLE

arcsinh(x)/(1 - x) = x/1! + 2*x^2/2! + 5*x^3/3! + 20*x^4/4! + 109*x^5/5! + ...

MAPLE

a:=series(arcsinh(x)/(1 - x), x=0, 24): seq(n!*coeff(a, x, n), n=0..23); # Paolo P. Lava, Mar 27 2019