A012314 Expansion of e.g.f. sec(arcsin(x)*log(x+1)).

1, 0, 0, 0, 12, -60, 450, -2940, 33488, -360864, 4785480, -62142960, 941944872, -14815408608, 260792820288, -4784515051680, 95341465939968, -1988764871186304, 44407627224011712, -1038296963667026304

Offset

0,5

Links

G. C. Greubel, Table of n, a(n) for n = 0..434

Example

E.g.f. = 1 + 12*x^4/4! - 60*x^5/5! + 450*x^6/6! - 2940*x^7/7! + ...

Maple

seq(coeff(series(factorial(n)*sec(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[Sec[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); Vec(serlaplace(1/cos(asin(x)*log(x+1)))) \\ G. C. Greubel, Oct 25 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( 1/Cos(Arcsin(x)*Log(x+1)) )); [Factorial(n-1)*b[n]: n in [1..m-1]]; // G. C. Greubel, Oct 25 2018

Crossrefs

Sequence in context: A009154 A012313 A012517 * A233004 A012360 A012708

Adjacent sequences: A012311 A012312 A012313 * A012315 A012316 A012317

Keyword

sign

Author

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

Status

approved