A296336 Expansion of e.g.f. log(1 + x*cos(x))*exp(x).
0, 1, 1, -1, 0, -16, -5, 13, -1512, 12336, -98177, 444773, 1249160, -75244508, 1296229779, -15956614403, 130892534160, 59122803744, -31478991643617, 837166840532589, -14900078660739984, 181343532181629332, -480411914937891389, -54306065912649098539, 2080183542455901881320
Offset: 0
Keywords
Examples
log(1 + x*cos(x))*exp(x) = x/1! + x^2/2! - x^3/3! - 16*x^5/5! - 5*x^6/6! + ...
Programs
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Maple
a:=series(log(1 + x*cos(x))*exp(x),x=0,25): seq(n!*coeff(a,x,n),n=0..24); # Paolo P. Lava, Mar 27 2019
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Mathematica
nmax = 24; CoefficientList[Series[Log[1 + x Cos[x]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]! -
PARI
x='x+O('x^99); concat([0], Vec(serlaplace(exp(x)*log(1+x*cos(x))))) \\ Altug Alkan, Dec 28 2017