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A159039
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E.g.f. sec(x)/(1-x) = 1/( cos(x) * (1-x) ).
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0
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1, 1, 3, 9, 41, 205, 1291, 9037, 73681, 663129, 6681811, 73499921, 884701817, 11501123621, 161215091675, 2418226375125, 38711013514145, 658087229740465, 11847975015003811, 225111525285072409, 4502600876889685705, 94554618414683399805, 2080270953997427933611
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OFFSET
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1,3
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LINKS
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FORMULA
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E.g.f.: sec(x)/(1-x) = 1/U(0) where U(k)= 1 - x/(1 - x/(x + (2*k+1)*(2*k+2)/U(k+1)) ; (continued fraction, 3-step). - Sergei N. Gladkovskii, Oct 17 2012
E.g.f.: (1-1/Q(0))/(1-x), where Q(k)= 1 - (2*k+1)*(2*k+2)/x^2 + 1/x^2*(2*k+1)*(2*k+2)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, May 01 2013
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MAPLE
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G(x):=sec(x)/(1-x): f[0]:=G(x): for n from 1 to 21 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..21); #
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MATHEMATICA
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CoefficientList[Series[1/(Cos[x]*(1-x)), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 27 2013 *)
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PROG
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(PARI) x='x+O('x^66); Vec(serlaplace(1/(cos(x)*(1-x)))) \\ Joerg Arndt, May 01 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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