A049215 - OEIS

%I #19 Aug 13 2024 14:35:50

%S 1,40,2464,229760,30633856,5561407488,1322489954304,399463775797248,

%T 149519094622027776,67960463478175825920,36884466463352967659520,

%U 23566236397584291201024000,17511732541318788803985408000

%N Scaled coefficients of (arctanh x)^4.

%F E.g.f.: (arctanh x)^4 or (1-x^2)^-1 * (arctanh x)^3.

%F a(n) is coefficient of x^(2*n+4) in (arctanh x)^4, multiplied by (2*n+4)!/4!.

%F a(n) = (1/8) * Sum_{p=1..2*n+3} binomial(2*n+2,p-1)*Sum_{m=4..2*n+4} binomial(m,4)*abs(s(2*n+4,m))*((-p)^(m-4)+(-p)^(m-4)) where s(n,m) is Stirling number of first kind . - _Ammar Khatab_, Aug 13 2024

%e (arctanh x)^4 = x^4 + 4/3*x^6 + 22/15*x^8 + 1436/945*x^10 + ...

%t a[n_] := SeriesCoefficient[ArcTanh[x]^4, {x, 0, 2n+4}]*(2n+4)!/4!;

%t a /@ Range[0, 12] (* _Jean-François Alcover_, Mar 26 2021 *)

%Y Cf. A049214, A049216, A049217.

%K nonn

%O 0,2

%A Joe Keane (jgk(AT)jgk.org)