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Number of permutations of [n] with exactly six occurrences of the consecutive step pattern up, down, down.
(history; published version)
#10 by Vaclav Kotesovec at Tue Aug 26 17:03:44 EDT 2014
STATUS

editing

approved

#9 by Vaclav Kotesovec at Tue Aug 26 16:51:45 EDT 2014
FORMULA

a(n) ~ c * (3*sqrt(3)/(2*Pi))^n * n! * n^6, where c = 0.000003054026651631929902... = c0 * (c0-1)^6 / (3^6 * 6!), and c0 = (1 + exp(Pi/sqrt(3))) * sqrt(3) / (2*Pi). - Vaclav Kotesovec, Aug 26 2014

STATUS

approved

editing

#8 by Vaclav Kotesovec at Tue Aug 26 10:37:28 EDT 2014
STATUS

editing

approved

#7 by Vaclav Kotesovec at Tue Aug 26 10:37:23 EDT 2014
FORMULA

a(n) ~ c * (3*sqrt(3)/(2*Pi))^n * n! * n^6, where c = 0.00000305402665163000003054026651631929902... . - Vaclav Kotesovec, Aug 26 2014

STATUS

approved

editing

#6 by Vaclav Kotesovec at Tue Aug 26 03:56:55 EDT 2014
STATUS

editing

approved

#5 by Vaclav Kotesovec at Tue Aug 26 03:56:50 EDT 2014
FORMULA

a(n) ~ c * (3*sqrt(3)/(2*Pi))^n * n! * n^6, where c = 0.00000305402665163... . - Vaclav Kotesovec, Aug 26 2014

STATUS

approved

editing

#4 by Alois P. Heinz at Wed Aug 20 22:23:07 EDT 2014
STATUS

editing

approved

#3 by Alois P. Heinz at Wed Aug 20 22:23:04 EDT 2014
LINKS

Alois P. Heinz, <a href="/A246251/b246251.txt">Table of n, a(n) for n = 19..160</a>

#2 by Alois P. Heinz at Wed Aug 20 17:11:25 EDT 2014
NAME

allocated for Alois P. Heinz

Number of permutations of [n] with exactly six occurrences of the consecutive step pattern up, down, down.

DATA

1488257158851, 176902009674966, 13166075391964578, 775944032960346939, 39844140679287441918, 1872063201155821139178, 82897279832156950225548, 3526803545750650310760216, 146090377422354615989531688, 5948505245302032452585146020, 239776137775416266444362226760

OFFSET

19,1

CROSSREFS

Column k=6 of A242819.

KEYWORD

allocated

nonn

AUTHOR

Alois P. Heinz, Aug 20 2014

STATUS

approved

editing

#1 by Alois P. Heinz at Wed Aug 20 16:43:12 EDT 2014
NAME

allocated for Alois P. Heinz

KEYWORD

allocated

STATUS

approved