A296741
Expansion of e.g.f. arcsin(x*sec(x)) (odd powers only).
Original entry on oeis.org
1, 4, 64, 2752, 237312, 34390016, 7512117248, 2302977392640, 942529341030400, 496287845973753856, 326775812392982937600, 263039306566659448242176, 254121613033387345942937600, 290175686081926976733941071872, 386599796043915196967089006968832
Offset: 0
arcsin(x*sec(x)) = x/1! + 4*x^3/3! + 64*x^5/5! + 2752*x^7/7! + 237312*x^9/9! + ...
Cf.
A001818,
A003700,
A009118,
A009119,
A009562,
A009563,
A009765,
A009843,
A102072,
A191003,
A296464,
A296466,
A296679,
A296680,
A296742,
A296743.
-
nmax = 15; Table[(CoefficientList[Series[ArcSin[x Sec[x]], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]
-
first(n) = x='x+O('x^(2*n)); vecextract(Vec(serlaplace(asin(x/cos(x)))), (4^n - 1)/3) \\ Iain Fox, Dec 19 2017
A296742
Expansion of e.g.f. arcsinh(x*sec(x)) (odd powers only).
Original entry on oeis.org
1, 2, 4, -8, 2448, 130976, -2342848, -239130240, 99052990720, 8918588764672, -2795242017684480, -92786315822417920, 279479081010906828800, -57316070780459900928, -39411396653183724314673152, 5932051008707372732672475136, 10689040617354387626585873252352
Offset: 0
arcsinh(x*sec(x)) = x/1! + 2*x^3/3! + 4*x^5/5! - 8*x^7/7! + 2448*x^9/9! + ...
Cf.
A001818,
A003700,
A009118,
A009119,
A009562,
A009563,
A009765,
A009843,
A102072,
A191003,
A296464,
A296466,
A296679,
A296680,
A296741,
A296743.
-
nmax = 17; Table[(CoefficientList[Series[ArcSinh[x Sec[x]], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]
-
first(n) = x='x+O('x^(2*n)); vecextract(Vec(serlaplace(asinh(x/cos(x)))), (4^n - 1)/3) \\ Iain Fox, Dec 19 2017
A302543
Expansion of e.g.f. arctanh(x)/cos(x) (odd powers only).
Original entry on oeis.org
1, 5, 69, 2001, 104073, 8723549, 1088372557, 190057979177, 44285819490065, 13267464006201781, 4964113699657822805, 2266816666007859759489, 1239999748307938170531225, 800189083150907165762837517, 601369618369661775955962338653, 520607107122686183781743903500505
Offset: 0
arctanh(x)/cos(x) = x/1! + 5*x^3/3! + 69*x^5/5! + 2001*x^7/7! + 104073*x^9/9! + ...
Cf.
A000182,
A000364,
A000795,
A002084,
A003701,
A003702,
A010050,
A012840,
A296743,
A301942,
A302444,
A302542.
-
nmax = 16; Table[(CoefficientList[Series[ArcTanh[x]/Cos[x], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]
Showing 1-3 of 3 results.