A296731
Expansion of e.g.f. sec(x*cos(x)) (even powers only).
Original entry on oeis.org
1, 1, -7, -119, 4241, 216241, -16578871, -1851684743, 236706675617, 48609995386849, -8951725537756135, -3042019551814333463, 738962020041708730673, 387782426903449423831441, -116858640965630479825258519, -90328812874963081877073927719
Offset: 0
sec(x*cos(x)) = 1 + x^2/2! - 7*x^4/4! - 119*x^6/6! + 4241*x^8/8! + ...
Cf.
A000364,
A009008,
A009009,
A009010,
A009011,
A009015,
A009016,
A009446,
A009447,
A009633,
A009634,
A102072,
A102075,
A191512,
A296728,
A296729,
A296730,
A296740.
-
nmax = 15; Table[(CoefficientList[Series[Sec[x Cos[x]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
-
first(n) = x='x+O('x^(2*n-2)); vecextract(Vec(serlaplace(1/cos(x*cos(x)))), (4^n - 1)/3) \\ Iain Fox, Dec 19 2017
A296740
Expansion of e.g.f. sec(x*cosh(x)) (even powers only).
Original entry on oeis.org
1, 1, 17, 481, 26529, 2355841, 304490801, 54346519137, 12784369495873, 3834072115634689, 1427927160049839185, 646549058811594306017, 349778819738933516544737, 222822626689237030117683841, 165094750167986500169166495089, 140768231241374238855897822250081
Offset: 0
sec(x*cosh(x)) = 1 + x^2/2! + 17*x^4/4! + 481*x^6/6! + 26529*x^8/8! + ...
Cf.
A000364,
A009008,
A009009,
A009010,
A009011,
A009015,
A009016,
A009446,
A009447,
A009633,
A009634,
A102072,
A102075,
A191512,
A296728,
A296729,
A296730,
A296731.
-
nmax = 15; Table[(CoefficientList[Series[Sec[x Cosh[x]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
-
first(n) = x='x+O('x^(2*n-2)); vecextract(Vec(serlaplace(1/cos(x*cosh(x)))), (4^n - 1)/3) \\ Iain Fox, Dec 19 2017
A296728
Expansion of e.g.f. arcsin(x*cos(x)) (odd powers only).
Original entry on oeis.org
1, -2, -16, 8, 12672, 571264, -44351360, -12355211520, -452681248768, 478190483394560, 132554796040912896, -18854516962334277632, -27186884683859043123200, -5502410397289951851773952, 6273206188133923322747420672, 5389680791235134726930445369344
Offset: 0
arcsin(x*cos(x)) = x/1! - 2*x^3/3! - 16*x^5/5! + 8*x^7/7! + 12672*x^9/9! + ...
Cf.
A001818,
A009015,
A009016,
A009446,
A009447,
A009633,
A009634,
A012495,
A012780,
A101928,
A191512,
A296464,
A296466,
A296679,
A296680,
A296729,
A296730,
A296731,
A296740.
-
nmax = 16; Table[(CoefficientList[Series[ArcSin[x Cos[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
A296729
Expansion of e.g.f. arcsin(x*cosh(x)) (odd powers only).
Original entry on oeis.org
1, 4, 44, 1912, 156816, 21506816, 4420845376, 1271132964480, 487161448339712, 239980527068474368, 147742478026391141376, 111153314734461183924224, 100339775128577885016985600, 107037870347952811373977239552, 133204585741561810426003651444736
Offset: 0
arcsin(x*cosh(x)) = x/1! + 4*x^3/3! + 44*x^5/5! + 1912*x^7/7! + 156816*x^9/9! + ...
Cf.
A001818,
A009015,
A009016,
A009446,
A009447,
A009633,
A009634,
A012495,
A012780,
A101928,
A191512,
A296464,
A296466,
A296679,
A296680,
A296728,
A296730,
A296731,
A296740.
-
nmax = 15; Table[(CoefficientList[Series[ArcSin[x Cosh[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*cosh(x)))), (4^n - 1)/3) \\ Iain Fox, Dec 19 2017
A296730
Expansion of e.g.f. arctanh(x*cos(x)) (odd powers only).
Original entry on oeis.org
1, -1, -31, -337, 24705, 2451679, -17936543, -42895630065, -5396647099903, 1239561882325439, 708575518706816481, 37448619025871342959, -113842057082636742446975, -52054011876398495316250977, 16226448322449614832534708065, 31975745831751940004484917311439
Offset: 0
arctanh(x*cos(x)) = x/1! - x^3/3! - 31*x^5/5! - 337*x^7/7! + 24705*x^9/9! + ...
Cf.
A000364,
A009015,
A009016,
A009446,
A009447,
A009633,
A009634,
A010050,
A012494,
A191512,
A296465,
A296467,
A296728,
A296729,
A296731,
A296740.
-
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}]
-
first(n) = x='x+O('x^(2*n)); vecextract(Vec(serlaplace(atanh(x*cos(x)))), (4^n - 1)/3) \\ Iain Fox, Dec 19 2017
Showing 1-5 of 5 results.