%I M5218 #23 Dec 01 2018 07:58:39
%S 0,30,217800,16294301520,6544151202877440,9764950519194817858560,
%T 42762698240957239228617722880,466476501707480855594001261422438400,
%U 11235366943887873286558941529247982529413120
%N Generalized tangent numbers of type 3^(2n+1).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Ira M. Gessel, <a href="http://dx.doi.org/10.1016/0097-3165(90)90060-A">Symmetric functions and P-recursiveness</a>, J. Combin. Theory Ser. A 53 (1990), no. 2, 257-285.
%F a(n) = 1/3^(2*n+1) * Sum_{i=0..2*n+1} (-1)^(i+1) * 2^-i * binomial(2*n+1, i) * A000182(n+i+1).
%F a(n) ~ 2^(1/2)*3^(-1/2)*Pi^(-1/2)*n^(-1/2)*2^(8*n)*3^(-3*n)*{1 - 13/144*n^-1 + 169/41472*n^-2 + 48635/17915904*n^-3 - ...}. - Joe Keane (jgk(AT)jgk.org), Nov 07 2003
%t a000182[n_] := (4^n*(4^n-1)*Abs[BernoulliB[2*n]])/(2*n); a[n_] := Sum[((-1)^(i+1)*Binomial[2*n+1, i]*a000182[n+i+1])/2^i, {i, 0, 2*n+1}]/3^(2*n+1)
%Y Cf. A000182 (tangent numbers).
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, _Simon Plouffe_
%E Edited by _Dean Hickerson_, Dec 10 2002
%E More terms from Joe Keane (jgk(AT)jgk.org), Nov 07 2003