A049217 E.g.f.: (arctanh(x))^6/6! (even powers only).

1, 112, 14448, 2393600, 510205696, 137602949120, 46060832825344, 18793914785464320, 9198585089011777536, 5325419604670079827968, 3602492652661227322343424, 2817222656974232498101813248, 2523030777997770071132105342976, 2566233198310773279287315980615680

Offset: 0

Author

Joe Keane (jgk(AT)jgk.org)

Keywords

• nonn
• easy

Examples

			(arctanh x)^6 = x^6 + 2*x^8 + 43/15*x^10 + 680/189*x^12 + ...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..80

Programs

Maple

a:= n-> (2*n+6)!* coeff(series(arctanh(x)^6/6!, x, 2*n+7), x, 2*n+6):
seq (a(n), n=0..20);  # Alois P. Heinz, Aug 25 2012

Mathematica

With[{nn=40, c=6!}, Take[CoefficientList[Series[ArcTanh[x]^6/c, {x, 0, nn}], x] Range[0, nn]!, {7, -1, 2}]] (* Harvey P. Dale, Aug 24 2012 *)

PARI

a(n) = polcoeff(serlaplace(atanh(x+O(x^24))^6)/6!,2*n+6)

Formula

E.g.f.: (arctanh x)^6/6! = sum(n>=0, a(n)*x^(2*n+6)/(2*n+6)! ).

Extensions

Definition clarified by Harvey P. Dale, Aug 24 2012.