A383987
Series expansion of the exponential generating function -tridend(-(1-exp(x))) where tridend(x) = (1 - 3*x - sqrt(1+6*x+x^2)) / (4*x) (A001003).
Original entry on oeis.org
0, 1, -5, 49, -725, 14401, -360005, 10863889, -384415925, 15612336481, -715930020005, 36592369889329, -2062911091119125, 127170577711282561, -8510569547826528005, 614491222512504748369, -47615614242877583230325, 3941408640018910366196641
Offset: 0
Cf.
A002050,
A006531,
A084099,
A101851,
A114285,
A225883,
A383985,
A383986,
A383988,
A383989,
A383991.
Composition of
A001003 with exp(x)-1.
-
nn = 17; f[x_] := (1 + 3*x - Sqrt[1 + 6*x + x^2])/(4*x); Range[0, nn]! * CoefficientList[Series[f[-(1 - Exp[x])], {x, 0, nn}], x]
A383989
Series expansion of the exponential generating function ff6^!(exp(x)-1) where ff6^!(x) = x * (1-3*x-x^2+x^3) / (1+3*x+x^2-x^3).
Original entry on oeis.org
0, 1, -11, 61, -467, 4381, -49091, 643021, -9615827, 161844541, -3026079971, 62243374381, -1396619164787, 33949401567901, -888725861445251, 24926889744928141, -745755560487363347, 23705772035082494461, -797875590555470224931, 28346366547928396344301
Offset: 0
Cf.
A002050,
A006531,
A084099,
A101851,
A114285,
A225883,
A383985,
A383986,
A383987,
A383988,
A383995.
-
nn = 19; f[x_] := x*(1 - 3*x - x^2 + x^3)/(1 + 3*x + x^2 - x^3);
Range[0, nn]! * CoefficientList[Series[f[-(1 - Exp[x])], {x, 0, nn}], x]
A383985
Series expansion of the exponential generating function LambertW(1-exp(x)), see A000169.
Original entry on oeis.org
0, 1, -1, 4, -23, 181, -1812, 22037, -315569, 5201602, -97009833, 2019669961, -46432870222, 1168383075471, -31939474693297, 942565598033196, -29866348653695203, 1011335905644178273, -36446897413531401020, 1392821757824071815641, -56259101478392975833333
Offset: 0
Cf.
A002050,
A006531,
A084099,
A101851,
A114285,
A177885,
A225883,
A383986,
A383987,
A383988,
A383989.
Composition of
A000169 with signs and 1-exp(x).
-
nn = 20; f[x_] := -Sum[k^(k - 1)*(1 - Exp[x])^k/k!, {k, nn}];
Range[0, nn]! * CoefficientList[Series[f[x], {x, 0, nn}], x]
A383988
Series expansion of the exponential generating function -postLie(1-exp(x)) where postLie(x) = -log((1 + sqrt(1-4*x)) / 2) (given by A006963).
Original entry on oeis.org
0, 1, -2, 12, -110, 1380, -22022, 426972, -9747950, 256176660, -7617417302, 252851339532, -9268406209790, 371843710214340, -16206868062692582, 762569209601624892, -38525315595630383630, 2079964082064837282420, -119513562475103977951862
Offset: 0
Cf.
A002050,
A006531,
A084099,
A097388,
A101851,
A114285,
A225883,
A383985,
A383986,
A383987,
A383989. Composition of -
A006963(-x) and exp(x)-1.
-
nn = 18; f[x_] := Log[(1 + Sqrt[1 + 4*x])/2];
Range[0, nn]! * CoefficientList[Series[f[-(1 - Exp[x])], {x, 0, nn}], x]
Showing 1-4 of 4 results.
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