A049216 Scaled coefficients of (arctanh x)^5.

1, 70, 6384, 804320, 136804096, 30459752960, 8632830664704, 3041109959196672, 1305140879116763136, 670935549630120394752, 407240889859179425562624, 288272814806050917816729600

Offset

0,2

Links

Table of n, a(n) for n=0..11.

Formula

E.g.f.: (arctanh x)^5 or (1-x^2)^-1 * (arctanh x)^4.

a(n) is coefficient of x^(2*n+5) in (arctanh x)^5, multiplied by (2*n+5)!/5!.

Example

(arctanh x)^5 = x^5 + 5/3*x^7 + 19/9*x^9 + 457/189*x^11 + ...

Mathematica

a[n_] := SeriesCoefficient[ArcTanh[x]^5, {x, 0, 2n+5}]*(2n+5)!/5!;
a /@ Range[0, 11] (* Jean-François Alcover, Mar 26 2021 *)

Crossrefs

Cf. A049214, A049215, A049217.

Sequence in context: A238540 A060057 A363296 * A229477 A213699 A184275

Adjacent sequences: A049213 A049214 A049215 * A049217 A049218 A049219

Keyword

nonn

Author

Joe Keane (jgk(AT)jgk.org)

Status

approved