A096718
Denominators of terms in series expansion of arcsin(arctan(x)).
Original entry on oeis.org
1, 6, 120, 5040, 362880, 4435200, 32947200, 145297152000, 69701632000, 13516122267648000, 5676771352412160000, 2872446304320552960000, 1723467782592331776000000, 1935799013407707050803200, 485144691014524112732160000, 1353553687930522274522726400000, 204193242064947360270857011200000
Offset: 0
arcsin(arctan(x)) = x - 1/6*x^3 + 13/120*x^5 - 341/5040*x^7 + 18649/362880*x^9 - 177761/4435200*x^11 + ...
-
Denominator[Take[CoefficientList[Series[ArcSin[ArcTan[x]], {x,0,40}], x], {2,-1,2}]] (* G. C. Greubel, Nov 17 2016 *)
A096717
Numerators of terms in series expansion of arcsin(arctan(x)).
Original entry on oeis.org
1, -1, 13, -341, 18649, -177761, 1087433, -4043494549, 1674761567, -284891766539657, 106410874319325461, -48402125366670946877, 26344930021064765797249, -27048608191991004321089, 6237195766537863970288933, -16102066950215127630856787159, 2258820895862623437612519923989
Offset: 0
arcsin(arctan(x)) = x - 1/6*x^3 + 13/120*x^5 - 341/5040*x^7 + 18649/362880*x^9 - 177761/4435200*x^11 + ...
Cf.
A096718,
A096664,
A096671,
A096712,
A096716,
A045688,
A045689,
A096719,
A096720,
A096721,
A096722.
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Numerator[Take[CoefficientList[Series[ArcSin[ArcTan[x]], {x,0,50}], x], {2, -1, 2}]] (* G. C. Greubel, Nov 17 2016 *)
A096722
Denominators of terms in series expansion of arcsin(arctan(x)) - arctan(arcsin(x)).
Original entry on oeis.org
1, 1, 1, 30, 756, 75600, 199584, 54486432000, 2421619200, 151227648000, 5913303492096000, 5203707073044480000, 512936840057241600000, 5041143264082570444800000, 1238175538546596249600000, 11695452372671563431936000000, 33500453776280426294437478400000, 44295044437526341433756221440000000
Offset: 0
arcsin(arctan(x)) - arctan(arcsin(x)) = -1/30*x^7 + 13/756*x^9 - 2329/75600*x^11 + 3749/199584*x^13 - 1405132357/54486432000*x^15 + ...
Cf.
A096721,
A096717,
A096718,
A096664,
A096671,
A096712,
A096716,
A045688,
A045689,
A096719,
A096720.
-
Denominator[Take[CoefficientList[Series[ArcSin[ArcTan[x]] - ArcTan[ArcSin[x]], {x,0,40}], x], {2,-1,2}]] (* G. C. Greubel, Nov 18 2016 *)
Showing 1-3 of 3 results.