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

0, 1, 0, 6, 0, 120, 0, 5040, 0, 362880, 0, 39916800, 0, 6227020800, 0, 1307674368000, 0, 355687428096000, 0, 121645100408832000, 0, 51090942171709440000, 0, 25852016738884976640000, 0

Offset: 0

Author

Russ Cox

Keywords

• nonn

Comments

Normally sequences like this are not included, since with the alternating 0's deleted it is already in the database.

From Michael Somos, Mar 04 2004: (Start)

Stirling transform of a(n) = [1,0,6,0,120,0,5040,...] is A089677(n) = [1,1,7,37,271,...].

Stirling transform of a(n-1) = [0,1,0,6,0,120,0,...] is A000670(n-1) = [0,1,3,13,75,...].

Stirling transform of a(n-1) = [1,1,0,6,0,120,0,...] is A052856(n-1) = [1,2,4,14,76,...]. (End)

References

• 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.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..448
• Index entries for sequences related to factorial numbers

Programs

Maple

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

Mathematica

nn = 20; Rest[ Range[0, nn]! CoefficientList[ Series[ Log[(1 - x^2)^(-1/2)], {x, 0, nn}], x]] (* Geoffrey Critzer, May 29 2013 *)
Riffle[Range[1,25,2]!,0,{1,-1,2}] (* Harvey P. Dale, Mar 10 2017 *)

PARI

a(n)=if(n<0,0,if(n%2,n!,0));

Formula

E.g.f.: -log(cos(arcsin(x))). - Vladimir Kruchinin, Jun 15 2011