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A007415
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Expand sin x / exp x = x-x^2+x^3/3-x^5/30+... and invert nonzero coefficients.
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5
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0, 1, -1, 3, 0, -30, 90, -630, 0, 22680, -113400, 1247400, 0, -97297200, 681080400, -10216206000, 0, 1389404016000, -12504636144000, 237588086736000, 0, -49893498214560000, 548828480360160000, -12623055048283680000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| a(n) = [n mod 4 > 0] * (-1)^(n+1+[n/4]) * n!/2^[n/2]. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 06 2004
E.g.f.: sin(x)/exp(x) =x-x^2/(G(0)+x); G(k)=2k+1-x+x*(2k+1)/(4k+3-x+x^2*(4k+3)/( (2k+2)*(4k+5)-x^2+x*(2k+2)*(4k+5)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Nov 20 2011
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CROSSREFS
| Absolute values are essentially the same as A046979, where zeros are replaced by ones.
a(4n+2) = -(-1)^n*A052277(n), a(2n+1) = (-1)^[n/2]*A007019(n).
Cf. A046981, A007452, A009775, A092820.
Sequence in context: A138543 A143769 A190963 * A145222 A058833 A012775
Adjacent sequences: A007412 A007413 A007414 * A007416 A007417 A007418
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KEYWORD
| sign
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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