A279238
Numerators of coefficients in expansion of (cos x)/(1 + cos(sqrt(x))).
Original entry on oeis.org
1, 1, -11, -343, 871, 54871, -12359, -102902159, -137687549, 344971369, 20000206271, -34379966953693, -452834430450401, 18163626705916771, 951418549566510481, -381881231033010506527, -4252976361755938012709, -218740547087902859463611
Offset: 0
(1/2) + (1/8)x - (11/48)x^2 - (343/5760)x^3 + ... ; 1/2, 1/3, -11/48, 1/6480, -343/5760, ... = A279238/A279239.
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z = 26; t = CoefficientList[Series[Cos[x]/(1 + Cos[Sqrt[x]]), {x, 0, z}], x];
Numerator[t] (* A279238 *)
Denominator[t] (* A279239 *)
%/2 (* A279240 *)
A279240
Denominators of coefficients in expansion of (2 cos x)/(1 + cos(sqrt(x))).
Original entry on oeis.org
1, 4, 24, 2880, 40320, 7257600, 479001600, 697426329600, 20922789888000, 261321375744000, 221172909834240000, 4496002911110430720000, 620448401733239439360000, 806582922253211271168000000, 304888344611713860501504000000, 4244045756995056938180935680000000
Offset: 0
(1/1) + (1/4)x - (11/24)x^2 - (343/2880)x^3 + (871/40320)x^4 + ... ; 1/1, 1/4, -11/24, -343/2880, ... = A279238/A279240.
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CoefficientList[Series[2 Cos[x]/(1+Cos[Sqrt[x]]),{x,0,20}],x]//Denominator (* Harvey P. Dale, Jun 05 2024 *)
A279370
Numerators of coefficients in expansion of (cos(sqrt(x)))/(1 + cos(sqrt(x))).
Original entry on oeis.org
1, -1, -1, -17, -31, -691, -5461, -929569, -3202291, -221930581, -4722116521, -56963745931, -14717667114151, -2093660879252671, -86125672563201181, -129848163681107301953, -868320396104950823611, -209390615747646519456961, -14129659550745551130667441
Offset: 0
(1/2) - (1/8)x - (1/48)x^2 - (17/5760)x^3 + ... ; 1/2, - 1/8, - 48/2, - 17/5760, ... = A279370/A279109.
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z = 26; t = CoefficientList[Series[Cos[Sqrt[x]]/(1 + Cos[Sqrt[x]]), {x, 0, z}], x];
Numerator[t] (* A279370 *)
Denominator[t] (* A279109 *)
A279256
Numerators of coefficients in expansion of (e^x)/(1 + cos(sqrt(x))).
Original entry on oeis.org
1, 5, 19, 977, 4469, 214171, 457321, 925684673, 4949391841, 493402195453, 14167601252171, 57190922263627, 69165140252515309, 11615975003110672871, 547719474074019696919, 54367007962729782596209, 6786547315820425430115737, 1769764154745747063102330217
Offset: 0
(1/2) + (5/8)x + (19/48)x^2 + (977/5760)x^3 + ... ; 1/2, 5/8, 19/48, 977/5760, ... = A279256/A279239.
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z = 26; t = CoefficientList[Series[E^x/(1 + Cos[Sqrt[x]]), {x, 0, z}], x];
Numerator[t] (* A279256 *)
Denominator[t] (* A279239 *)
A279306
Numerators of coefficients in expansion of (cosh(x))/(1 + cos(sqrt(x))).
Original entry on oeis.org
1, 1, 13, 377, 2551, 97711, 1686481, 447824017, 2522468131, 22174988051, 7129179751261, 1852107834946547, 34648570480339663, 828888380086508653, 273996480127378324681, 462007733994120695494433, 308514276772559961052721, 38471181499444351991058251
Offset: 0
(1/2) + (1/8)x + (13/48)x^2 + (377/5760)x^3 + ... ; 1/2, 1/8, 13/48, 377/5760, ... = A279306/A279239.
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z = 30; t = CoefficientList[Series[Cosh[x]/(1 + Cos[Sqrt[x]]), {x, 0, z}], x];
Numerator[t] (* A279306 *)
Denominator[t] (* A279239 *)
A279307
Numerators of coefficients in expansion of (sinh x)/(1 + cos(sqrt(x))).
Original entry on oeis.org
0, 1, 1, 5, 137, 647, 22951, 328201, 26965819, 135880897, 37044323689, 91760237711, 250120070812867, 235374750708709, 38112363401091809, 1747698886011364219, 2880212454433162868027, 1444514603466022486187, 54349494835431693600323
Offset: 0
(0/1) + (1/2)x + (1/8)x^2 + (5/48)x^3 + ... ; 0/1, 1/2, 1/8, 5/48, ... = A279307/A279239.
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z = 30; t = CoefficientList[Series[Sinh[x]/(1 + Cos[Sqrt[x]]), {x, 0, z}], x];
Numerator[t] (* A279307 *)
Denominator[t] (* A279239 *)
Showing 1-6 of 6 results.
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