login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A296979 Expansion of e.g.f. arcsin(log(1 + x)). 3
0, 1, -1, 3, -12, 68, -480, 4144, -42112, 494360, -6581880, 98079696, -1617373296, 29245459176, -575367843960, 12235339942344, -279650131845120, 6836254328079936, -177979145883651648, 4916243253642325056, -143602294106947553280, 4422411460743707222784 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..21.

FORMULA

a(n) ~ -(-1)^n * n^(n-1) / (exp(1) - 1)^(n - 1/2). - Vaclav Kotesovec, Mar 26 2019

EXAMPLE

arcsin(log(1 + x)) = x^1/1! - x^2/2! + 3*x^3/3! - 12*x^4/4! + 68*x^5/5! - 480*x^6/6! + ...

MAPLE

a:=series(arcsin(log(1+x)), x=0, 22): seq(n!*coeff(a, x, n), n=0..21); # Paolo P. Lava, Mar 26 2019

MATHEMATICA

nmax = 21; CoefficientList[Series[ArcSin[Log[1 + x]], {x, 0, nmax}], x] Range[0, nmax]!

nmax = 21; CoefficientList[Series[-I Log[I Log[1 + x] + Sqrt[1 - Log[1 + x]^2]], {x, 0, nmax}], x] Range[0, nmax]!

CROSSREFS

Cf. A001710, A001818, A003703, A003708, A009024, A009454, A009775, A104150, A189815, A296980, A296981, A296982.

Sequence in context: A187118 A121812 A039750 * A004127 A058115 A101313

Adjacent sequences:  A296976 A296977 A296978 * A296980 A296981 A296982

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Dec 22 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 13 12:57 EDT 2022. Contains 356091 sequences. (Running on oeis4.)