login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A001456 Number of permutations of length n with longest increasing subsequence of length 5.
(Formerly M5183 N2251)
3
1, 25, 421, 6105, 83029, 1100902, 14516426, 192422979, 2579725656, 35098717902, 485534447114, 6835409506841, 97966603326993, 1429401763567226, 21226755241285022, 320692032888290224, 4926576077469905280, 76913478420068425515, 1219520974164038038455 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,2

REFERENCES

J. M. Hammersley, A few seedings of research, in Proc. Sixth Berkeley Sympos. Math. Stat. and Prob., ed. L. M. le Cam et al., Univ. Calif. Press, 1972, Vol. I, pp. 345-394.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 5..700 (first 100 terms from Alois P. Heinz)

R. M. Baer and P. Brock, Natural sorting over permutation spaces, Math. Comp. 22 1968 385-410.

FORMULA

Recurrence: (n-5)*(n+3)^3*(n+4)^2*(n+6)^2*(11025*n^8 + 25515*n^7 - 286443*n^6 - 161641*n^5 + 2585080*n^4 - 59048*n^3 - 7819612*n^2 + 146328*n + 7254720)*a(n) = (n+3)^2*(606375*n^14 + 6629175*n^13 - 3194685*n^12 - 243068077*n^11 - 448185134*n^10 + 2897169968*n^9 + 6909605819*n^8 - 18854806947*n^7 - 49141228309*n^6 + 52949408689*n^5 + 157003723774*n^4 - 31022236184*n^3 - 177627829824*n^2 - 22499155440*n + 46832450400)*a(n-1) - (n-1)*(11278575*n^15 + 107036370*n^14 - 128493459*n^13 - 3499379232*n^12 - 3757671198*n^11 + 38759610078*n^10 + 60611718946*n^9 - 233170832954*n^8 - 421914005785*n^7 + 715791177016*n^6 + 1483014906497*n^5 - 861954416990*n^4 - 2293879983512*n^3 + 206528474736*n^2 + 1232273843856*n + 13490305056)*a(n-2) + (n-2)^2*(n-1)*(84286125*n^13 + 498481200*n^12 - 2434626540*n^11 - 13242031168*n^10 + 26565838790*n^9 + 116444106688*n^8 - 166166829480*n^7 - 520627558844*n^6 + 548244457053*n^5 + 1265779705376*n^4 - 798189974324*n^3 - 1219994476884*n^2 + 526747368888*n + 238058922240)*a(n-3) - 2*(n-3)^2*(n-2)^2*(n-1)*(116181450*n^11 + 631786995*n^10 - 3196642374*n^9 - 12497984441*n^8 + 40113159004*n^7 + 67582342915*n^6 - 249420026774*n^5 - 74467478051*n^4 + 592968590146*n^3 - 201054848490*n^2 - 142917171372*n - 573108048)*a(n-4) + 14400*(n-4)^2*(n-3)^3*(n-2)^2*(n-1)*(11025*n^8 + 113715*n^7 + 200862*n^6 - 727084*n^5 - 854995*n^4 + 4446427*n^3 + 2445184*n^2 - 7589778*n + 1695924)*a(n-5). - Vaclav Kotesovec, Mar 16 2014

a(n) ~ 9 * 5^(2*n+25/2) / (2^9 * Pi^2 * n^12). - Vaclav Kotesovec, Mar 16 2014

CROSSREFS

Column k=5 of A047874.

Sequence in context: A025975 A025953 A020595 * A021964 A022456 A020593

Adjacent sequences:  A001453 A001454 A001455 * A001457 A001458 A001459

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Alois P. Heinz, Jul 01 2012

Name of the sequence clarified by Vaclav Kotesovec, Mar 18 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 19 17:55 EDT 2018. Contains 316376 sequences. (Running on oeis4.)