cp's OEIS Frontend

A320959 The exponential limit of arctanh (odd indices only).

%I A320959 #17 Jul 23 2019 04:27:11
%S A320959 1,10,1248,631440,852647040,2462394816000,13241729554099200,
%T A320959 120563962753538304000,1733764260005567741952000,
%U A320959 37343395325946891151466496000,1155311729350231354981936496640000,49626886713956000390638096497377280000,2878005957927359237424925417166882734080000
%N A320959 The exponential limit of arctanh (odd indices only).
%C A320959 See A320956 for definitions and comments.
%F A320959 For n >= 3 and odd, -a(m)*Zeta(m) = g(n), where g denotes the exponential limit of log(Gamma(x + 1)) and m = (n-1)/2.
%e A320959 Illustration of the convergence in the sense of A320956:
%e A320959    [0] 0, 0, 0,  0, 0,    0, 0,      0, 0,         0, ...
%e A320959    [1] 0, 1, 0,  2, 0,   24, 0,    720, 0,     40320, ... A005359
%e A320959    [2] 0, 1, 0,  8, 0,  384, 0,  46080, 0,  10321920, ... A067624
%e A320959    [3] 0, 1, 0, 10, 0,  984, 0, 262800, 0, 132289920, ...
%e A320959    [4] 0, 1, 0, 10, 0, 1224, 0, 514800, 0, 445576320, ...
%e A320959    [5] 0, 1, 0, 10, 0, 1248, 0, 615600, 0, 725840640, ...
%e A320959    [6] 0, 1, 0, 10, 0, 1248, 0, 630720, 0, 832527360, ...
%e A320959    [7] 0, 1, 0, 10, 0, 1248, 0, 631440, 0, 851155200, ...
%e A320959    [8] 0, 1, 0, 10, 0, 1248, 0, 631440, 0, 852606720, ...
%e A320959    [9] 0, 1, 0, 10, 0, 1248, 0, 631440, 0, 852647040, ...
%p A320959 # The function ExpLim is defined in A320956.
%p A320959 L := [ExpLim(28, arctanh)]: seq(L[2*n], n=1..13);
%t A320959 m = 13; CoefficientList[ArcTanh[x] + O[x]^(2 m + 1), x]*Range[0, 2 m - 1]!*BellB[Range[0, 2 m - 1]] // DeleteCases[#, 0]& (* _Jean-François Alcover_, Jul 23 2019 *)
%Y A320959 Cf. A320955 (exp), A320962 (log(x+1)), A320956 (sec+tan), A320958 (arcsin), this sequence (arctanh).
%Y A320959 Cf. A005359, A067624.
%K A320959 nonn
%O A320959 0,2
%A A320959 _Peter Luschny_, Nov 08 2018