A296940
Expansion of e.g.f. sech(x*tan(x/2)) (even powers only).
Original entry on oeis.org
1, 0, -3, -15, 406, 14355, -189123, -42283696, -837846615, 284972761557, 28521503291230, -3070544172379761, -1054107683427761463, 1143265731049052000, 54900209444888714822181, 7959249060310612253252265, -3679623847504649619798598778, -1631286181830482909037469295781
Offset: 0
sech(x*tan(x/2)) = 1 - 3*x^4/4! - 15*x^6/6! + 406*x^8/8! + ...
Cf.
A000364,
A001469,
A009011,
A110501,
A296839,
A296841,
A296842,
A296853,
A296854,
A296856,
A296939.
-
nmax = 17; Table[(CoefficientList[Series[Sech[x Tan[x/2]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
A296941
Expansion of e.g.f. arcsin(x*tan(x/2)) (even powers only).
Original entry on oeis.org
0, 1, 1, 18, 227, 12125, 542448, 55071205, 5492843269, 905996551626, 159770279801855, 39299019878991521, 10721872262093222016, 3707660329253983397113, 1438816154956071399594457, 668949924061617421125859650, 348908555505788456739965412203
Offset: 0
arcsin(x*tan(x/2)) = x^2/2! + x^4/4! + 18*x^6/6! + 227*x^8/8! + ...
Cf.
A001469,
A001818,
A012780,
A110501,
A296839,
A296841,
A296842,
A296853,
A296854,
A296856,
A296939,
A296940,
A296942.
-
nmax = 16; Table[(CoefficientList[Series[ArcSin[x Tan[x/2]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
A296942
Expansion of e.g.f. arcsinh(x*tan(x/2)) (even powers only).
Original entry on oeis.org
0, 1, 1, -12, -193, 5195, 397248, -9589391, -3147743231, -10931156748, 65632780196255, 4713930109297211, -2846093176389647904, -606335605925899344287, 213167747093485780707937, 109460864600185764327567060, -21782399212761670190907400897
Offset: 0
arcsinh(x*tan(x/2)) = x^2/2! + x^4/4! - 12*x^6/6! - 193*x^8/8! + ...
Cf.
A000364,
A001469,
A001818,
A110501,
A296839,
A296841,
A296842,
A296853,
A296854,
A296856,
A296939,
A296940,
A296941.
-
nmax = 16; Table[(CoefficientList[Series[ArcSinh[x Tan[x/2]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
Showing 1-3 of 3 results.