A012283 Expansion of e.g.f. arctan(sin(x)*log(x+1)).

0, 0, 2, -3, 4, -20, -130, 1869, -12280, 100080, -362822, -7482475, 168953420, -2715677172, 34715587062, -205932278475, -3285394779888, 157209810212416, -4031590864355982, 71565905502128781

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..440

Example

E.g.f. = 2*x^2/2! - 3*x^3/3! + 4*x^4/4! - 20*x^5/5! + ...

Mathematica

CoefficientList[Series[ArcTan[Log[1 + x]*Sin[x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 05 2015 *)

Prog

(PARI) x='x+O('x^30); concat([0, 0], Vec(serlaplace(atan(sin(x)* log(x+1))))) \\ G. C. Greubel, Oct 26 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Arctan(Sin(x)*Log(x+1)) )); [0, 0] cat [Factorial(n+1)*b[n]: n in [1..m-2]]; // G. C. Greubel, Oct 26 2018

Crossrefs

Sequence in context: A107241 A012576 A012579 * A012286 A302610 A331558

Adjacent sequences: A012280 A012281 A012282 * A012284 A012285 A012286

Keyword

sign

Author

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

Extensions

Prepended missing a(0)=a(1)=0 from Vaclav Kotesovec, Feb 05 2015

Status

approved