A296853
Expansion of e.g.f. tanh(x*tan(x/2)) (even powers only).
Original entry on oeis.org
0, 1, 1, -27, -403, 8345, 688473, -208019, -3189211931, -162605047455, 28806493001105, 5257860587364341, -288068264497990179, -230932276247139756887, -14420179324444754436023, 13944106915630111553887485, 3643613240568912544562868053
Offset: 0
tanh(x*tan(x/2)) = x^2/2! + x^4/4! - 27*x^6/6! - 403*x^8/8! + 8345*x^10/10! + ...
-
nmax = 16; Table[(CoefficientList[Series[Tanh[x Tan[x/2]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
A296854
Expansion of e.g.f. sinh(x*tan(x/2)) (even powers only).
Original entry on oeis.org
0, 1, 1, 18, 227, 4565, 126648, 4620805, 213569269, 12165013026, 835868220455, 68093897815361, 6483538063860336, 712877916658802713, 89586864207214060057, 12753583150716684461970, 2040805972702652020364603, 364567588100855831300341565
Offset: 0
sinh(x*tan(x/2)) = x^2/2! + x^4/4! + 18*x^6/6! + 227*x^8/8! + 4565*x^10/10! + ...
-
nmax = 17; Table[(CoefficientList[Series[Sinh[x Tan[x/2]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
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}]
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 1-6 of 6 results.