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A081123 a(n) = floor(n/2)!. 9
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 (list; graph; refs; listen; history; text; internal format)
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. 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

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Last modified April 5 13:26 EDT 2020. Contains 333241 sequences. (Running on oeis4.)