A012950 a(n) = (2n+1)! * [x^(2n+1)]; expansion of arcsin(tan(x)+arcsin(x)).

2, 11, 433, 47777, 10445209, 3792307917, 2060929368925, 1565891035323617, 1584908855099457809, 2061186455316106953685, 3349214731529157234143461, 6649249948563897129719525769, 15836980365691934720682871441241, 44569352711436570809863777097634621

Offset

0,1

Links

Table of n, a(n) for n=0..13.

Maple

a:= n-> (2*n+1)! *coeff(series(arcsin(tan(x)+arcsin(x)), x, 2*n+2), x, 2*n+1): seq(a(n), n=0..20);

Mathematica

Partition[CoefficientList[Series[ArcSin[Tan[x] + ArcSin[x]], {x, 0, 23}], x]*Range[0, 23]!, 2][[All, 2]]
With[{nn=30}, Take[CoefficientList[Series[ArcSin[Tan[x]+ArcSin[x]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Jul 21 2024 *)

Prog

(PARI) x='x+O('x^33); /* that many terms */
v=Vec(serlaplace(asin(tan(x)+asin(x)))); /* every second term is zero */
vector(#v\2, n, v[2*n-1]) /* show terms */
/* Joerg Arndt, Mar 16 2011 */

Crossrefs

Sequence in context: A052290 A145512 A013046 * A012979 A013109 A120934

Adjacent sequences: A012947 A012948 A012949 * A012951 A012952 A012953

Keyword

nonn

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Status

approved