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A009747 E.g.f. tan(x)*sinh(x) (even powers only).

%I A009747 #24 Apr 12 2017 23:09:13
%S A009747 0,2,12,142,3192,116282,6219972,458790022,44625674352,5534347077362,
%T A009747 852334810990332,159592488559874302,35703580441464231912,
%U A009747 9405575479317650316842,2881823738166957609703092,1016124476854507687644180982,408525180980254462140262747872,185768439922172208338308590282722
%N A009747 E.g.f. tan(x)*sinh(x) (even powers only).
%H A009747 G. C. Greubel, <a href="/A009747/b009747.txt">Table of n, a(n) for n = 0..240</a>
%H A009747 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>
%F A009747 a(n) ~ (2*n)! * 4^(n+1) * sinh(Pi/2) / Pi^(2*n+1). - _Vaclav Kotesovec_, Jan 24 2015
%t A009747 nn = 20; Table[(CoefficientList[Series[Sinh[x]*Tan[x], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* _Vaclav Kotesovec_, Jan 24 2015 *)
%o A009747 (Sage) # Generalized algorithm of L. Seidel (1877)
%o A009747 def A009747_list(n) :
%o A009747     R = []; A = {-1:0, 0:0}
%o A009747     k = 0; e = 1
%o A009747     for i in range(2*n) :
%o A009747         Am = 1 if e == -1 else 0
%o A009747         A[k + e] = 0
%o A009747         e = -e
%o A009747         for j in (0..i) :
%o A009747             Am += A[k]
%o A009747             A[k] = Am
%o A009747             k += e
%o A009747         if e == -1 : R.append(A[-i//2])
%o A009747     return R
%o A009747 A009747_list(10) # _Peter Luschny_, Jun 02 2012
%o A009747 (PARI) x='x+O('x^66); v=Vec(serlaplace(tan(x)*sinh(x))); concat([0],vector(#v\2,n,v[2*n-1])) \\ _Joerg Arndt_, Apr 26 2013
%Y A009747 Bisection of A009739 and (apparently) A062161.
%K A009747 nonn
%O A009747 0,2
%A A009747 _R. H. Hardin_
%E A009747 Extended and signs tested by _Olivier Gérard_, Mar 15 1997