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A163626
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The n-th derivative of the logistic function written in terms of y, where y=1/(1+exp(-x))
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0
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1, 1, -1, 1, -3, 2, 1, -7, 12, -6, 1, -15, 50, -60, 24, 1, -31, 180, -390, 360, -120, 1, -63, 602, -2100, 3360, -2520, 720, 1, -127, 1932, -10206, 25200, -31920, 20160, -5040, 1, -255, 6050, -46620, 166824, -317520, 332640, -181440, 40320, 1, -511, 18660
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Triangle T(n,k), read by rows, given by (1,0,2,0,3,0,4,0,5,0,6,0,7,0,8,0,9,...)DELTA (-1,-1,-2,-2,-3,-3,-4,-4,-5,-5,-6,-6,...) where DELTA is the operator defined in A084938. - From DELEHAM Philippe, Nov 05 2011
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EXAMPLE
| y=1/(1+exp(-x)) y^(0)=y y^(1)=y-y^2 y^(2)=y-3*y^2+2*y^3 y^(3)=y-7*y^2+12*y^3-6*y^4
Triangle begins :
1
1, -1
1, -3, 2
1, -7, 12, -6
1, -15, 50, -60, 24
1, -31, 180, -390, 360, -120
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CROSSREFS
| A028246
Sequence in context: A056151 A134436 A186370 * A028246 A082038 A143774
Adjacent sequences: A163623 A163624 A163625 * A163627 A163628 A163629
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KEYWORD
| easy,sign,tabl
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AUTHOR
| Richard Scholtz (rscholtz(AT)ufl.edu), Aug 01 2009
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