A012311 Expansion of e.g.f. tanh(arcsin(x)*log(x+1)).

0, 0, 2, -3, 12, -40, -2, 1281, -20328, 247176, -2577798, 24949485, -189717660, 500394960, 24648965430, -804228701535, 18028676700720, -340430894094480, 5649443088034290, -76409572412090115, 580555717060321980

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..446

Example

E.g.f. = 2*x^2/2! - 3*x^3/3! + 12*x^4/4! - 40*x^5/5! + ...

Maple

seq(coeff(series(factorial(n)*tanh(arcsin(x)*log(x+1)), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 25 2018

Mathematica

With[{nn=20}, CoefficientList[Series[Tanh[ArcSin[x]Log[x+1]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Feb 05 2013 *)

Prog

(PARI) x='x+O('x^30); concat([0, 0], Vec(serlaplace(tanh(asin(x)* log(x+1))))) \\ G. C. Greubel, Oct 25 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Tanh(Arcsin(x)*Log(x+1)) )); [0, 0] cat [Factorial(n+1)*b[n]: n in [1..m-2]]; // G. C. Greubel, Oct 25 2018

Crossrefs

Sequence in context: A268561 A352099 A012307 * A012513 A012515 A012510

Adjacent sequences: A012308 A012309 A012310 * A012312 A012313 A012314

Keyword

sign

Author

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

Extensions

Prepended two zeros, Joerg Arndt, Feb 05 2013

Status

approved