%I #18 Aug 25 2012 06:53:24
%S 1,112,14448,2393600,510205696,137602949120,46060832825344,
%T 18793914785464320,9198585089011777536,5325419604670079827968,
%U 3602492652661227322343424,2817222656974232498101813248,2523030777997770071132105342976,2566233198310773279287315980615680
%N E.g.f.: (arctanh(x))^6/6! (even powers only).
%H Alois P. Heinz, <a href="/A049217/b049217.txt">Table of n, a(n) for n = 0..80</a>
%F E.g.f.: (arctanh x)^6/6! = sum(n>=0, a(n)*x^(2*n+6)/(2*n+6)! ).
%e (arctanh x)^6 = x^6 + 2*x^8 + 43/15*x^10 + 680/189*x^12 + ...
%p a:= n-> (2*n+6)!* coeff(series(arctanh(x)^6/6!, x, 2*n+7), x, 2*n+6):
%p seq (a(n), n=0..20); # _Alois P. Heinz_, Aug 25 2012
%t 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 *)
%o (PARI) a(n) = polcoeff(serlaplace(atanh(x+O(x^24))^6)/6!,2*n+6)
%K nonn,easy
%O 0,2
%A Joe Keane (jgk(AT)jgk.org)
%E Definition clarified by _Harvey P. Dale_, Aug 24 2012.