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A073410 Number of permutations p of (1,2,3,...,n) such that 1*(-1)^p(1)+2*(-1)^p(2)+3*(-1)^p(3)+...+n*(-1)^p(n)=0. 0
0, 0, 2, 8, 0, 0, 576, 4608, 0, 0, 2505600, 30067200, 0, 0, 53444966400, 855119462400, 0, 0, 3587014803456000, 71740296069120000, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Equivalently the number of grand Dyck n-paths in which each run length is selected from {1..2*n} without replacement. - David Scambler, Apr 16 2013

LINKS

Table of n, a(n) for n=1..22.

FORMULA

It seems that a(n)=0 if n==1 or 2 (mod 4) and a(4*k)=4*k*a(4*k-1). - Benoit Cloitre, Aug 23 2002

PROG

(PARI) a(n)=sum(k=1, n!, if(sum(i=1, n, i*(-1)^component(numtoperm(n, k), i)), 0, 1))

CROSSREFS

Sequence in context: A230915 A242922 A242530 * A021361 A199156 A073001

Adjacent sequences:  A073407 A073408 A073409 * A073411 A073412 A073413

KEYWORD

nonn,more

AUTHOR

Benoit Cloitre, Aug 23 2002

EXTENSIONS

More terms from John W. Layman, Feb 05 2003

a(14)-a(22) from Robert Gerbicz, Nov 22 2010

STATUS

approved

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Last modified July 26 07:06 EDT 2014. Contains 244924 sequences.