A306254
Denominators of the rational factor of Kaplan's series for the Dottie number.
Original entry on oeis.org
4, 768, 61440, 165150720, 47563407360, 669692775628800, 417888291992371200, 2808209322188734464000, 3055331742541343096832000, 33437550590372458851729408000, 56175084991825730870905405440000, 7276695809501137874093602599075840000, 17464069942802730897824646237782016000000
Offset: 0
The Kaplan series begins with d = Pi/4 - Pi^3/768 - Pi^5/61440 - 43*Pi^7/165150720 - ...
- Amiram Eldar, Table of n, a(n) for n = 0..100
- Ozaner Hansha, The Dottie Number.
- Ozaner Hansha, Kaplan's series.
- Samuel R. Kaplan, The Dottie Number, Mathematics Magazine, Vol. 80, No. 1 (2007), pp. 73-74, alternative link.
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f[x_] := x - Cos[x]; g[x_] := InverseFunction[f][x]; s = {}; Do[AppendTo[s, Denominator[(-1/2)^n * 1/n! * Derivative[n][g][Pi/2]]], {n, 1, 30, 2}]; s
A362406
Denominators of the expansion of the series reversion of sin(x) + x, odd powers only.
Original entry on oeis.org
2, 96, 1920, 1290240, 92897280, 326998425600, 51011754393600, 85699747381248000, 23310331287699456000, 63777066403145711616000, 26786367889321198878720000, 867449737727777704488468480000, 520469842636666622693081088000000, 5845917272495039506088686780416000000
Offset: 0
f^-1(x) = (1/2)*x + (1/96)*x^3 + (1/1920)*x^5 + (43/1290240)*x^7 + ...
A362407
Numerators of the expansion of the series reversion of sin(x) + x, odd powers only.
Original entry on oeis.org
1, 1, 1, 43, 223, 60623, 764783, 107351407, 2499928867, 596767688063, 22200786516383, 64470807442488761, 3504534741776035061, 3597207408242668198973, 268918457620309807441853, 185388032403184965693274807, 18241991360742724891839902347
Offset: 0
f^-1(x) = (1/2)*x + (1/96)*x^3 + (1/1920)*x^5 + (43/1290240)*x^7 + ...
Showing 1-3 of 3 results.
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