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A297009 Expansion of e.g.f. arcsin(x*exp(x)). 3
0, 1, 2, 4, 16, 104, 816, 7792, 89216, 1177920, 17603200, 294334976, 5442281472, 110221745152, 2426850793472, 57718658411520, 1474590580228096, 40274407232294912, 1171043235561185280, 36115912820342407168, 1177554628069200035840, 40471207964013864124416 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

EXAMPLE

arcsin(x*exp(x)) = x^1/1! + 2*x^2/2! + 4*x^3/3! + 16*x^4/4! + 104*x^5/5! + 816*x^6/6! + ...

MATHEMATICA

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

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

PROG

(PARI) first(n) = x='x+O('x^n); Vec(serlaplace(asin(exp(x)*x)), -n) \\ Iain Fox, Dec 23 2017

CROSSREFS

Cf. A001818, A009017, A009121, A009448, A009565, A009635, A009768, A191719, A216401, A297010.

Sequence in context: A066318 A066952 A281964 * A135249 A318154 A110365

Adjacent sequences:  A297006 A297007 A297008 * A297010 A297011 A297012

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 23 2017

STATUS

approved

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Last modified January 16 21:37 EST 2019. Contains 319206 sequences. (Running on oeis4.)