A278562 Numerators of coefficients in Taylor series expansion of log(arcsin(x)/log(x+1)).

0, 1, -1, 1, -5, 19, -6863, 751, -3191, 2857, -467605, 434293, -79370603, 8181904909, -564351550729, 5044289, -15949219262783, 5026792806787, -6536042124050878927, 69028763155644023, -250300132038361463, 1022779523247467, -109243524012284271443941

Offset

0,5

Links

G. C. Greubel, Table of n, a(n) for n = 0..445

Example

The Taylor series begins (1/2)*x - (1/24)*x^2 + (1/8)*x^3 - (5/192)*x^4 + (19/288)*x^5 - (6863/362880)*x^6 + (751/17280)*x^7 - (3191/215040)*x^8 + (2857/89600)*x^9 - (467605/38320128)*x^10 + (434293/17418240)*x^11 - (79370603/7664025600)*x^12 + (8181904909/402361344000)*x^13 + ...

Mathematica

Numerator[CoefficientList[Series[Log[ArcSin[x]/Log[x + 1]], {x, 0, 50}], x]] (* G. C. Greubel, Aug 09 2018 *)

Crossrefs

Cf. A013568, A278563.

Sequence in context: A174490 A280034 A270486 * A013531 A357517 A122152

Adjacent sequences: A278559 A278560 A278561 * A278563 A278564 A278565

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 23 2016

Status

approved