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