A081123 a(n) = floor(n/2)!.

1, 1, 1, 1, 2, 2, 6, 6, 24, 24, 120, 120, 720, 720, 5040, 5040, 40320, 40320, 362880, 362880, 3628800, 3628800, 39916800, 39916800, 479001600, 479001600, 6227020800, 6227020800, 87178291200, 87178291200, 1307674368000, 1307674368000, 20922789888000, 20922789888000

Offset

0,5

Comments

This is the product of the first parts of the partitions (as nondecreasing list of parts) of n with exactly two positive integer parts, n > 1. - Wesley Ivan Hurt, Jan 25 2013

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n) = floor(n/2)!.

E.g.f.: 1+sqrt(Pi)/2*(x+2)*exp(x^2/4)*erf(x/2). - Vladeta Jovovic, Sep 25 2003

From Sergei N. Gladkovskii, Jul 28 2012: (Start)

G.f. G(0) where G(k) = 1 + x/(1 - x*(k+1)/( x*(k+1) + 1/G(k+1))); (continued fraction, 3rd kind, 3-step ).

E.g.f. 1 + sqrt(Pi)/2*(x+2)*exp(x^2/4)*erf(x/2) = 1 + x/(G(0)-x) where G(k) = 2*k + 1 + x - (2*k+1)*x/(x + 2 - 2*x/G(k+1)); (continued fraction, 1st kind, 2-step).

(End)

G.f.: U(0) where U(k) = 1 + x/(1 - x*(k+2)/(x*(k+2) + 1/U(k+1))); (continued fraction, 3-step). - Sergei N. Gladkovskii, Oct 23 2012

G.f.: U(0) where U(k) = 1 + x/((2*k+1) - x*(2*k+1)/(x + 2*1/U(k+1))) ; (continued fraction, 3-step). - Sergei N. Gladkovskii, Oct 23 2012

G.f.: 1 + x*G(0) where G(k) = 1 + x*(k+1)/(1 - x/(x + 1/G(k+1))); (continued fraction, 3-step). - Sergei N. Gladkovskii, Nov 18 2012

Example

a(8) = 24, since 8 has 4 nondecreasing partitions with exactly two positive integer parts: (1,7),(2,6),(3,5),(4,4).  Multiplying the first parts of these partitions together, we get: (1)(2)(3)(4) = 4! = 24. - Wesley Ivan Hurt, Jun 03 2013

Maple

a:=n->floor(n/2)!: seq(a(k), k=1..70); # Wesley Ivan Hurt, Jun 03 2013

Mathematica

Table[(Floor[n/2])!, {n, 0, 40}] (* Vincenzo Librandi, Aug 06 2013 *)

Prog

(Magma) [Factorial(Floor(n/2)): n in [0..40]]; // Vincenzo Librandi, Aug 06 2013
(PARI) for(n=0, 50, print1((n\2)!, ", ")) \\ G. C. Greubel, Aug 01 2017

Crossrefs

Cf. A000142, A004526, A081124, A081125.

Sequence in context: A129881 A132369 A282169 * A056038 A076929 A265642

Adjacent sequences: A081120 A081121 A081122 * A081124 A081125 A081126

Keyword

easy,nonn

Author

Paul Barry, Mar 07 2003

Status

approved