A294313
Expansion of e.g.f. sech(x*exp(x)).
Original entry on oeis.org
1, 0, -1, -6, -19, 20, 899, 7966, 27705, -366552, -8374201, -80690302, 9794597, 16015845820, 317370642315, 2554368906150, -37571987331343, -1784464543440304, -31315944840101233, -80221319702865398, 12685422355781995485, 422083364962616527716
Offset: 0
sech(x*exp(x)) = 1 - x^2/2! - 6*x^3/3! - 19*x^4/4! + 20*x^5/5! + 899*x^6/6! + ...
Cf.
A000364,
A009017,
A009121,
A009301,
A009448,
A009565,
A009635,
A009768,
A191719,
A216401,
A217502,
A294312,
A296544,
A297009,
A297010.
-
a:=series(sech(x*exp(x)),x=0,22): seq(n!*coeff(a,x,n),n=0..21); # Paolo P. Lava, Mar 27 2019
-
nmax = 21; CoefficientList[Series[Sech[x Exp[x]], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 21; CoefficientList[Series[1/Cosh[x Exp[x]], {x, 0, nmax}], x] Range[0, nmax]!
A296543
Expansion of e.g.f. tanh(exp(x)-1).
Original entry on oeis.org
0, 1, 1, -1, -11, -33, 61, 1367, 7253, -12561, -580499, -4701497, 4669765, 580325215, 6636339165, 1365901495, -1122870368715, -17289945450289, -31110588453299, 3713822629274023, 74717183313957413, 280555705771423039, -19253195126787261507, -496715617694137066089, -3008746115751273626347
Offset: 0
tanh(exp(x)-1) = x/1! + x^2/2! - x^3/3! - 11*x^4/4! - 33*x^5/5! + 61*x^6/6! + 1367*x^7/7! + ...
-
a:=series(tanh(exp(x)-1),x=0,25): seq(n!*coeff(a,x,n),n=0..24); # Paolo P. Lava, Mar 27 2019
-
nmax = 24; CoefficientList[Series[Tanh[Exp[x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 24; CoefficientList[Series[Sinh[Exp[x] - 1]/Cosh[Exp[x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 24; CoefficientList[Series[(Exp[x] - 1)/(1 + ContinuedFractionK[(Exp[x] - 1)^2, 2 k - 1, {k, 2, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
Showing 1-2 of 2 results.