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A074143 a(1) = 1; a(n) = n * sum {a(k) | k < n}. 11
1, 2, 9, 48, 300, 2160, 17640, 161280, 1632960, 18144000, 219542400, 2874009600, 40475635200, 610248038400, 9807557760000, 167382319104000, 3023343138816000, 57621363351552000, 1155628453883904000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is also the number of elements of the alternating semigroup (A^c_n) for F(n, p) if p = n - 1 (cf. A001710). - Bakare Gatta Naimat, Jan 15 2016

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Stephen Lipscomb, Symmetric inverse semigroups, Mathematical surveys and monographs, Vol.46 Amer. Math. Soc. (1996).

FORMULA

a(n) = n^2*a(n-1)/(n-1) for n > 2.

a(n) = n*ceiling[n!/2] = n*A001710(n-1) = A001710(n+1)-A001710(n) = ceiling[A001563(n)/2] - Henry Bottomley, Nov 27 2002

a(n) = ((n+1)!-n!)/2 for n > 1. - Vladimir Joseph Stephan Orlovsky, Apr 03 2011

G.f.: (U(0) + x)/(2*x)  where U(k)=  1 - 1/(k+1 - x*(k+1)^2*(k+2)/(x*(k+1)*(k+2) - 1/U(k+1))) ; (continued fraction, 3-step). - Sergei N. Gladkovskii, Sep 27 2012

G.f.: 1/2 + Q(0), where Q(k)= 1 - 1/(k+2 - x*(k+2)^2*(k+3)/(x*(k+2)*(k+3)-1/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, Apr 19 2013

a(n) = sum(j = 0..n, (-1)^(n-j)*binomial(n, j)*(j)^(n+1))/(n+1), n > 1, a(1) = 1. -  Vladimir Kruchinin, Jun 01 2013

a(n) = numerator(n!/2*n). - Vincenzo Librandi, Apr 15 2014

a(n) is F(n;p) = n^2(n-1)!/2 if p = n-1 in A^c_n. For instance for n=4 and p=n-1: F(4; 4-1)= 4^2(4-1)!/2 = 16*6/2 = 48. - Bakare Gatta Naimat, Nov 18 2015

MAPLE

seq(sum(mul(j, j=3..n), k=1..n), n=1..19); # Zerinvary Lajos, Jun 01 2007

a := n -> `if`(n=1, 1, n!*n/2): seq(a(n), n=1..19); # Peter Luschny, Jan 22 2016

MATHEMATICA

A074143[1] = 1; A074143[n_] := A074143[n] = n * Sum[a[k], {k, n - 1}]; Array[A074143, 20] (* T. D. Noe, Apr 05 2011 *)

Table[Numerator[n!/2 n], {n, 40}] (* Vincenzo Librandi, Apr 15 2014)

PROG

(MAGMA) [Numerator(Factorial(n)/2*n): n in [1..30]]; // Vincenzo Librandi, Apr 15 2014

CROSSREFS

A diagonal of A254040.

Cf. A001563, A001710.

Sequence in context: A171803 A100427 A214404 * A198892 A205571 A052826

Adjacent sequences:  A074140 A074141 A074142 * A074144 A074145 A074146

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Aug 28 2002

EXTENSIONS

More terms from Henry Bottomley, Nov 27 2002

STATUS

approved

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Last modified November 17 05:59 EST 2018. Contains 317275 sequences. (Running on oeis4.)