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A013459
Expansion of e.g.f. exp(arctan(x) - log(x+1)).
1
1, 0, 1, -4, 9, -40, 385, -2700, 15505, -145360, 1886625, -19796500, 190881625, -2654379000, 44269902625, -625468889500, 8553276590625, -156119043652000, 3194978818578625, -57041478987070500
OFFSET
0,4
LINKS
FORMULA
From Robert Israel, Jan 29 2018: (Start)
E.g.f.: exp(arctan(x) - log(x+1)).
(n+1)^2*(n+2)*a(n)+n*(n+2)*a(n+1)+(n+2)*a(n+2)+a(n+3) = 0. (End)
MAPLE
f:= gfun:-rectoproc({(n+1)^2*(n+2)*a(n)+n*(n+2)*a(n+1)+(n+2)*a(n+2)+a(n+3) = 0, a(0)=1, a(1)=0, a(2)=1}, a(n), remember):
map(f, [$0..40]); # Robert Israel, Jan 29 2018
MATHEMATICA
With[{nn=20}, CoefficientList[Series[Exp[ArcTan[x]-Log[x+1]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Dec 03 2011 *)
PROG
(PARI) a(n)=polcoeff(exp(atan(x))/(1+x), n)*n! \\ Jaume Oliver Lafont, Oct 24 2009
CROSSREFS
Sequence in context: A073414 A085110 A374939 * A041229 A042887 A053908
KEYWORD
sign
AUTHOR
Patrick Demichel (patrick.demichel(AT)hp.com)
EXTENSIONS
Edited by Robert Israel, Jan 29 2018
STATUS
approved