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A297211
Expansion of e.g.f. log(1 + arctan(x))*exp(-x).
3
0, 1, -3, 6, -8, 13, -103, 462, 824, -8239, -147747, 1233518, 12148288, -127674419, -2090702391, 24495009510, 410685350032, -5514147250815, -111860639828131, 1673006899192118, 37306857729115304, -619246417449233555, -15476404474443728487, 281907759055194714206
OFFSET
0,3
EXAMPLE
log(1 + arctan(x))*exp(-x) = x/1! - 3*x^2/2! + 6*x^3/3! - 8*x^4/4! + 13*x^5/5! - 103*x^6/6! + ...
MAPLE
a:=series(log(1+arctan(x))*exp(-x), x=0, 24): seq(n!*coeff(a, x, n), n=0..23); # Paolo P. Lava, Mar 26 2019
MATHEMATICA
nmax = 23; CoefficientList[Series[Log[1 + ArcTan[x]] Exp[-x], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 23; CoefficientList[Series[Log[1 + (I/2) (Log[1 - I x] - Log[1 + I x])] Exp[-x], {x, 0, nmax}], x] Range[0, nmax]!
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Dec 27 2017
STATUS
approved