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A012474
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Expansion of arcsin(cos(x)*sin(x)) = x - 3/3!*x^3 - 15/5!*x^5 + 357/7!*x^7 + 22305/9!*x^9...
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0
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1, -3, -15, 357, 22305, -582483, -217683375, -2001865323, 7258418490945, 826442897487837, -580853295560646735, -204631967729205027003, 85920364932388858911585, 79053144190920049745846157
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OFFSET
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0,2
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LINKS
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FORMULA
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E.g.f.: arcsin(cos(x)*sin(x)) = sum a(n)x^(2n+1)/(2n+1)!.
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MATHEMATICA
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With[{nn=30}, Take[CoefficientList[Series[ArcSin[Cos[x]Sin[x]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Jul 18 2021 *)
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PROG
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(PARI) a(n)=local(sx); if(n<0, 0, sx=sin(x+O(x^(2*n+2))); (2*n+1)!*polcoeff(subst(serreverse(sx), x, subst(sx, x, x*2)/2), 2*n+1))
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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Patrick Demichel (patrick.demichel(AT)hp.com)
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STATUS
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approved
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