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
A296743
Expansion of e.g.f. arctanh(x*sec(x)) (odd powers only).
Original entry on oeis.org
1, 5, 109, 5977, 612729, 100954061, 24395453861, 8128143367905, 3571195811862385, 2000535014776893973, 1391684597704875555165, 1177047158822263838854889, 1189444022487013498606939625, 1415364934488337503351305867997, 1958850511524588636608881908473749
Offset: 0
arctanh(x*sec(x)) = x/1! + 5*x^3/3! + 109*x^5/5! + 5977*x^7/7! + 612729*x^9/9! + ...
Cf.
A003700,
A009118,
A009119,
A009562,
A009563,
A009765,
A009843,
A010050,
A102075,
A191003,
A296465,
A296467,
A296741,
A296742.
-
nmax = 15; Table[(CoefficientList[Series[ArcTanh[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(atanh(x/cos(x)))), (4^n - 1)/3) \\ Iain Fox, Dec 19 2017
A302444
Expansion of e.g.f. arcsinh(x)/cos(x) (odd powers only).
Original entry on oeis.org
1, 2, 24, 216, 15936, -77056, 90991744, -8523712768, 2731708067840, -684815907467264, 268028469798256640, -114888252320482000896, 62022733722259702579200, -38635369828053720937463808, 28349537098304682205749968896, -23874826868622028919177351004160
Offset: 0
arcsinh(x)/cos(x) = x/1! + 2*x^3/3! + 24*x^5/5! + 216*x^7/7! + 15936*x^9/9! - 77056*x^11/11! + ...
Cf.
A000182,
A000364,
A000795,
A001818,
A002084,
A003701,
A003702,
A012821,
A296742,
A301942,
A302542,
A302543.
-
nmax = 16; Table[(CoefficientList[Series[ArcSinh[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.