A059239 Numerators of coefficients of asymptotic expansion related to iterated sine function.

1, 1, 3, 2, 3, 18, 1382, 12, 32553, 87734, 1047666, 2796588, 1418184546, 23685516, 366420255876, 13785346041608, 23127963123651, 2729316555918, 52630543106106954746, 1850522471899932, 4699488932936084196918, 18241171727016849632292, 91090700441348806587348

Offset

0,3

References

N. G. de Bruijn, Asymptotic Methods in Analysis, North-Holland, 3rd. ed., 1970; see p. 158, (8.6.4).

Links

G. C. Greubel, Table of n, a(n) for n = 0..314

Formula

a(n) = numerator ( (1-2*n)*(-12)^n*Bernoulli(2*n)/(2*n)! ).

Example

1, 1, 3/5, 2/7, 3/25, 18/385, 1382/79625, 12/1925, 32553/14889875, 87734/116491375, 1047666/4094715625, 2796588/32534376875 = A059239/A059240.

Maple

a:= n-> numer((1-2*n)*(-12)^n*bernoulli(2*n)/(2*n)!): seq (a(n), n=0..30);

Mathematica

Numerator[Table[(1 - 2*n)*(-12)^n*BernoulliB[2*n]/(2*n)!, {n, 0, 25}]] (* G. C. Greubel, Jan 02 2017 *)

Crossrefs

Cf. A059240.

Sequence in context: A059366 A298594 A092950 * A350517 A123170 A253381

Adjacent sequences: A059236 A059237 A059238 * A059240 A059241 A059242

Keyword

nonn,easy,frac

Author

N. J. A. Sloane, Jan 21 2001

Status

approved