A012310 Expansion of e.g.f. arcsinh(arcsin(x) * log(x+1)).

0, 0, 2, -3, 12, -40, 118, 21, -5208, 88416, -904518, 8456085, -36204300, -582795720, 25175931870, -566080291035, 10469521737360, -151909726765440, 1439879949016050, 12663393759659565, -1154176350734965860

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..436

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)*arcsinh(arcsin(x)*log(x+1)), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 25 2018

Mathematica

With[{nn = 30}, CoefficientList[Series[ArcSinh[ArcSin[x] Log[x + 1]], {x, 0, nn}], x] Range[0, nn]!] (* G. C. Greubel, Oct 25 2018 *)

Prog

(PARI) x='x+O('x^30); concat([0, 0], Vec(serlaplace(asinh(asin(x)* log(x+1))))) \\ G. C. Greubel, Oct 25 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Argsinh(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: A012513 A012515 A012510 * A082526 A151368 A087650

Adjacent sequences: A012307 A012308 A012309 * A012311 A012312 A012313

Keyword

sign

Author

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

Extensions

a(0) and a(1) inserted and title improved by Sean A. Irvine, Jul 17 2018

Status

approved