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A012317
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Expansion of e.g.f. arcsin(arcsin(x) * exp(x)).
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1
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0, 1, 2, 5, 20, 133, 1070, 10705, 125512, 1717321, 26518138, 459336605, 8787628060, 184388779469, 4205082557286, 103631769297641, 2743399950572304, 77654985344871313, 2340183966373322610
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OFFSET
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0,3
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LINKS
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Robert Israel, Table of n, a(n) for n = 0..410
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EXAMPLE
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E.g.f. = x + 2/2!*x^2 + 5/3!*x^3 + 20/4!*x^4 + 133/5!*x^5 ...
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MAPLE
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S:= series(arcsin(arcsin(x)*exp(x)), x, 51):
seq(coeff(S, x, j)*j!, j=0..50); # Robert Israel, Oct 25 2018
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MATHEMATICA
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With[{nmax = 30}, CoefficientList[Series[ArcSin[ArcSin[x]*Exp[x]], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Oct 25 2018 *)
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PROG
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(PARI) x='x+O('x^30); concat([0], Vec(serlaplace( asin(asin(x)*exp(x))))) \\ G. C. Greubel, Oct 25 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Arcsin(Arcsin(x)*Exp(x)))); [0] cat [Factorial(n)*b[n]: n in [1..m-1]]; // G. C. Greubel, Oct 25 2018
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CROSSREFS
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Sequence in context: A130293 A156073 A006366 * A297630 A297629 A118181
Adjacent sequences: A012314 A012315 A012316 * A012318 A012319 A012320
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KEYWORD
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nonn
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AUTHOR
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Patrick Demichel (patrick.demichel(AT)hp.com)
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EXTENSIONS
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a(0) inserted and title improved by Sean A. Irvine, Jul 17 2018
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STATUS
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approved
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