cp's OEIS Frontend

A005212 n! if n is odd otherwise 0 (from the Taylor series for sin x).

%I A005212 #41 Jun 23 2017 21:26:51
%S A005212 0,1,0,6,0,120,0,5040,0,362880,0,39916800,0,6227020800,0,
%T A005212 1307674368000,0,355687428096000,0,121645100408832000,0,
%U A005212 51090942171709440000,0,25852016738884976640000,0
%N A005212 n! if n is odd otherwise 0 (from the Taylor series for sin x).
%C A005212 Normally sequences like this are not included, since with the alternating 0's deleted it is already in the database.
%C A005212 From _Michael Somos_, Mar 04 2004: (Start)
%C A005212 Stirling transform of a(n) = [1,0,6,0,120,0,5040,...] is A089677(n) = [1,1,7,37,271,...].
%C A005212 Stirling transform of a(n-1) = [0,1,0,6,0,120,0,...] is A000670(n-1) = [0,1,3,13,75,...].
%C A005212 Stirling transform of a(n-1) = [1,1,0,6,0,120,0,...] is A052856(n-1) = [1,2,4,14,76,...]. (End)
%D A005212 D. R. Hofstadter, Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought, (together with the Fluid Analogies Research Group), NY: Basic Books, 1995.
%H A005212 G. C. Greubel, <a href="/A005212/b005212.txt">Table of n, a(n) for n = 0..448</a>
%H A005212 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F A005212 E.g.f.: -log(cos(arcsin(x))). - _Vladimir Kruchinin_, Jun 15 2011
%p A005212 BB:=[T,{T=Prod(Z,F),F=Sequence(B),B=Prod(Z,Z)}, labeled]: seq(count(BB,size=i),i=0..24); # _Zerinvary Lajos_, Apr 22 2007
%t A005212 nn = 20; Rest[ Range[0, nn]! CoefficientList[ Series[ Log[(1 - x^2)^(-1/2)], {x, 0, nn}], x]] (* _Geoffrey Critzer_, May 29 2013 *)
%t A005212 Riffle[Range[1,25,2]!,0,{1,-1,2}] (* _Harvey P. Dale_, Mar 10 2017 *)
%o A005212 (PARI) a(n)=if(n<0,0,if(n%2,n!,0));
%K A005212 nonn
%O A005212 0,4
%A A005212 _Russ Cox_