A296939
Expansion of e.g.f. sec(x*tan(x/2)) (even powers only).
Original entry on oeis.org
1, 0, 3, 15, 644, 17145, 1124673, 74115496, 7730031915, 921044459943, 145334164141820, 26830525240048761, 6053646614467427553, 1586816790903080698000, 487642998132913180824819, 171640559783810345998524735, 69078935661419038650738789428
Offset: 0
sec(x*tan(x/2)) = 1 + 3*x^4/4! + 15*x^6/6! + 644*x^8/8! + ...
Cf.
A000364,
A001469,
A009010,
A110501,
A296839,
A296841,
A296842,
A296853,
A296854,
A296856,
A296940.
-
nmax = 16; Table[(CoefficientList[Series[Sec[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.