A012474 Expansion of arcsin(cos(x)*sin(x)) = x - 3/3!*x^3 - 15/5!*x^5 + 357/7!*x^7 + 22305/9!*x^9...

1, -3, -15, 357, 22305, -582483, -217683375, -2001865323, 7258418490945, 826442897487837, -580853295560646735, -204631967729205027003, 85920364932388858911585, 79053144190920049745846157

Offset

0,2

Links

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

Formula

E.g.f.: arcsin(cos(x)*sin(x)) = sum a(n)x^(2n+1)/(2n+1)!.

Mathematica

With[{nn=30}, Take[CoefficientList[Series[ArcSin[Cos[x]Sin[x]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Jul 18 2021 *)

Prog

(PARI) a(n)=local(sx); if(n<0, 0, sx=sin(x+O(x^(2*n+2))); (2*n+1)!*polcoeff(subst(serreverse(sx), x, subst(sx, x, x*2)/2), 2*n+1))

Crossrefs

Sequence in context: A029758 A103031 A338183 * A336270 A296940 A193119

Adjacent sequences: A012471 A012472 A012473 * A012475 A012476 A012477

Keyword

sign

Author

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

Status

approved