A005212 a(n) = 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, 15511210043330985984000000, 0, 10888869450418352160768000000, 0, 8841761993739701954543616000000

Offset

0,4

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

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A000142, A000670, A005359, A052856, A089677.

Sequence in context: A085511 A187525 A187696 * A167028 A246137 A052679

Adjacent sequences: A005209 A005210 A005211 * A005213 A005214 A005215

Keyword

nonn

Author

Russ Cox

Status

approved