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Expansion of e.g.f. log(1 + x*sec(x))*exp(x).
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3
0, 1, 1, 5, 0, 64, -245, 2757, -23576, 272256, -3270977, 45055845, -671589952, 10984688636, -193875825117, 3688182769117, -75085512079184, 1630385857436224, -37596306847103457, 917765946045581357, -23641953753495247624, 640958728426947233468, -18242640219843554954221
EXAMPLE
log(1 + x*sec(x))*exp(x) = x/1! + x^2/2! + 5*x^3/3! + 64*x^5/5! - 245*x^6/6! + ...
MAPLE
a:=series(log(1+x*sec(x))*exp(x), x=0, 23): seq(n!*coeff(a, x, n), n=0..22); # Paolo P. Lava, Mar 27 2019
MATHEMATICA
nmax = 22; CoefficientList[Series[Log[1 + x Sec[x]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
Expansion of e.g.f. log(1 + x*sech(x))*exp(x).
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3
0, 1, 1, -1, 0, 4, -5, 13, -392, 2112, 7663, -165067, 1011560, -2965756, -11164309, 630876517, -12760548400, 133046910432, -189966787521, -18567623055795, 392188656574896, -5061972266268844, 33655544331988203, 565132153437469165, -26647451471277927416
EXAMPLE
log(1 + x*sech(x))*exp(x) = x/1! + x^2/2! - x^3/3! + 4*x^5/5! - 5*x^6/6! + ...
MAPLE
a:=series(log(1+x*sech(x))*exp(x), x=0, 25): seq(n!*coeff(a, x, n), n=0..24); # Paolo P. Lava, Mar 27 2019
MATHEMATICA
nmax = 24; CoefficientList[Series[Log[1 + x Sech[x]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
Expansion of e.g.f. log(1 + x*cosh(x))*exp(x).
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3
0, 1, 1, 5, 0, 44, -245, 1917, -17976, 191760, -2268017, 29862645, -432485152, 6819543964, -116400819509, 2138673633397, -42078450265744, 882702459984256, -19667723002057473, 463866294631620941, -11545312970532620104, 302416006623761207804, -8316019118849688156693
EXAMPLE
log(1 + x*cosh(x))*exp(x) = x/1! + x^2/2! + 5*x^3/3! + 44*x^5/5! - 245*x^6/6! + ...
MAPLE
a:=series(log(1 + x*cosh(x))*exp(x), x=0, 23): seq(n!*coeff(a, x, n), n=0..22); # Paolo P. Lava, Mar 26 2019
MATHEMATICA
nmax = 22; CoefficientList[Series[Log[1 + x Cosh[x]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
PROG
(PARI) x='x+O('x^99); concat([0], Vec(serlaplace(exp(x)*log(1+x*cosh(x))))) \\ Altug Alkan, Dec 28 2017
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