A009448
E.g.f. sin(x*exp(x)).
Original entry on oeis.org
0, 1, 2, 2, -8, -84, -504, -2304, -6656, 15760, 484000, 5348320, 44393856, 288642368, 1137006976, -5372233216, -195241910272, -2961479980800, -34259767672320, -320473550808576, -2158264400250880, -1727938748171264, 278774033845987328
Offset: 0
-
With[{nn=30},CoefficientList[Series[Sin[x Exp[x]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Mar 17 2012 *)
-
a(n):=sum(binomial(n,2*j+1)*(2*j+1)^(n-2*j-1)*(-1)^j,j,0,(n-1)/2); /* Vladimir Kruchinin, Jun 10 2011 */
A191719
Expansion of e.g.f. arctan(x*exp(x)).
Original entry on oeis.org
0, 1, 2, 1, -20, -151, -354, 6217, 100472, 537777, -7631270, -223395919, -2120164188, 22050300505, 1154262915638, 17130776734905, -105423782758544, -11372993234072863, -245877012220234446, 345837436238423521, 188329590656514108380
Offset: 0
-
Rest[CoefficientList[Series[ArcTan[x*Exp[x]],{x,0,20}],x]*Range[0,20]!] (* Vaclav Kotesovec, Jan 02 2014 *)
-
a(n):=n!*sum(((2*m-1)^(n-2*m)*(-1)^(m-1))/(n-2*m+1)!,m,1,(n+1)/2);
A297010
Expansion of e.g.f. arcsinh(x*exp(x)).
Original entry on oeis.org
0, 1, 2, 2, -8, -76, -264, 1672, 36800, 261648, -1443680, -66164704, -792152448, 2482671424, 289529373056, 5294082629760, 1648955815936, -2474170098704128, -65494141255724544, -303927676523118080, 35926135133071923200, 1341060635191667045376
Offset: 0
arcsinh(x*exp(x)) = x^1/1! + 2*x^2/2! + 2*x^3/3! - 8*x^4/4! - 76*x^5/5! - 264*x^6/6! + ...
-
a:=series(arcsinh(x*exp(x)),x=0,22): seq(n!*coeff(a,x,n),n=0..21); # Paolo P. Lava, Mar 26 2019
-
nmax = 21; CoefficientList[Series[ArcSinh[x Exp[x]], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 21; CoefficientList[Series[Log[x Exp[x] + Sqrt[1 + x^2 Exp[2 x]]], {x, 0, nmax}], x] Range[0, nmax]!
-
first(n) = my(x='x+O('x^n)); Vec(serlaplace(asinh(exp(x)*x)), -n) \\ Iain Fox, Dec 23 2017
A294312
Expansion of e.g.f. sec(x*exp(x)).
Original entry on oeis.org
1, 0, 1, 6, 29, 180, 1501, 14434, 154265, 1856232, 24953401, 368767102, 5936244533, 103519338780, 1944554725205, 39134556793050, 840024295910833, 19157944025344464, 462629389438242673, 11792248121970820598, 316398168231432879565, 8913743651504295251844
Offset: 0
sec(x*exp(x)) = 1 + x^2/2! + 6*x^3/3! + 29*x^4/4! + 180*x^5/5! + 1501*x^6/6! + ...
Cf.
A000364,
A009007,
A009017,
A009121,
A009300,
A009448,
A009565,
A009635,
A009768,
A139134,
A191719,
A216401,
A217502,
A294313,
A297009,
A297010.
-
a:=series(sec(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[Sec[x Exp[x]], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 21; CoefficientList[Series[1/Cos[x Exp[x]], {x, 0, nmax}], x] Range[0, nmax]!
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]!
Showing 1-5 of 5 results.