A294314
Expansion of e.g.f. log(1 + x*sec(x))*exp(x).
Original entry on oeis.org
0, 1, 1, 5, 0, 64, -245, 2757, -23576, 272256, -3270977, 45055845, -671589952, 10984688636, -193875825117, 3688182769117, -75085512079184, 1630385857436224, -37596306847103457, 917765946045581357, -23641953753495247624, 640958728426947233468, -18242640219843554954221
Offset: 0
log(1 + x*sec(x))*exp(x) = x/1! + x^2/2! + 5*x^3/3! + 64*x^5/5! - 245*x^6/6! + ...
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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
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nmax = 22; CoefficientList[Series[Log[1 + x Sec[x]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
A296336
Expansion of e.g.f. log(1 + x*cos(x))*exp(x).
Original entry on oeis.org
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
log(1 + x*cos(x))*exp(x) = x/1! + x^2/2! - x^3/3! - 16*x^5/5! - 5*x^6/6! + ...
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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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nmax = 24; CoefficientList[Series[Log[1 + x Cos[x]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
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x='x+O('x^99); concat([0], Vec(serlaplace(exp(x)*log(1+x*cos(x))))) \\ Altug Alkan, Dec 28 2017
A297206
Expansion of e.g.f. log(1 + x*cosh(x))*exp(x).
Original entry on oeis.org
0, 1, 1, 5, 0, 44, -245, 1917, -17976, 191760, -2268017, 29862645, -432485152, 6819543964, -116400819509, 2138673633397, -42078450265744, 882702459984256, -19667723002057473, 463866294631620941, -11545312970532620104, 302416006623761207804, -8316019118849688156693
Offset: 0
log(1 + x*cosh(x))*exp(x) = x/1! + x^2/2! + 5*x^3/3! + 44*x^5/5! - 245*x^6/6! + ...
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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
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nmax = 22; CoefficientList[Series[Log[1 + x Cosh[x]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
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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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