login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A047890 Number of permutations in S_n with longest increasing subsequence of length <= 5. 10
1, 2, 6, 24, 120, 719, 5003, 39429, 344837, 3291590, 33835114, 370531683, 4285711539, 51990339068, 657723056000, 8636422912277, 117241501095189, 1639974912709122, 23570308719710838, 347217077020664880, 5231433025400049936, 80466744544235325387 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..250

F. Bergeron and F. Gascon, Counting Young tableaux of bounded height, J. Integer Sequences, Vol. 3 (2000), #00.1.7.

Alin Bostan, Andrew Elvey Price, Anthony John Guttmann, Jean-Marie Maillard, Stieltjes moment sequences for pattern-avoiding permutations, arXiv:2001.00393 [math.CO], 2020.

Shalosh B. Ekhad, Nathaniel Shar, and Doron Zeilberger, The number of 1...d-avoiding permutations of length d+r for SYMBOLIC d but numeric r, arXiv:1504.02513, 2015.

Ira M. Gessel, Symmetric functions and P-recursiveness, J. Combin. Theory Ser. A 53 (1990), no. 2, 257-285.

Nathaniel Shar, Experimental methods in permutation patterns and bijective proof, PhD Dissertation, Mathematics Department, Rutgers University, May 2016.

Index entries for sequences related to Young tableaux.

FORMULA

a(n) ~ 9 * 5^(2*n + 25/2) / (512 * n^12 * Pi^2). - Vaclav Kotesovec, Sep 10 2014

MAPLE

h:= proc(l) local n; n:=nops(l); add(i, i=l)! /mul(mul(1+l[i]-j

+add(`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n)

end:

g:= proc(n, i, l)

`if`(n=0 or i=1, h([l[], 1$n])^2, `if`(i<1, 0,

add(g(n-i*j, i-1, [l[], i$j]), j=0..n/i)))

end:

a:= n-> g(n, 5, []):

seq(a(n), n=1..30); # Alois P. Heinz, Apr 10 2012

# second Maple program

a:= proc(n) option remember; `if`(n<6, n!, ((-375+400*n+843*n^2

+322*n^3+35*n^4)*a(n-1) +225*(n-1)^2*(n-2)^2*a(n-3)

-(259*n^2+622*n+45)*(n-1)^2*a(n-2))/ ((n+6)^2*(n+4)^2))

end:

seq(a(n), n=1..30); # Alois P. Heinz, Sep 26 2012

MATHEMATICA

h[l_] := With[{n = Length[l]}, Sum[i, {i, l}]!/Product[Product[1+l[[i]]-j+Sum[If[l[[k]] >= j, 1, 0], {k, i+1, n}], {j, 1, l[[i]]}], {i, 1, n}]]; g[n_, i_, l_] := If[n == 0 || i == 1, h[Join[l, Array[1&, n]]]^2, If[i<1, 0, Sum[g[n-i*j, i-1, Join[l, Array[i&, j]]], {j, 0, n/i}]]]; a[n_, k_] := If[k >= n, n!, g[n, k, {}]]; Table[a[n, 5], {n, 1, 30}] (* Jean-François Alcover, Mar 10 2014, after Alois P. Heinz *)

CROSSREFS

A column of A047888. Cf. A005802, A052399.

Column k=5 of A214015.

Sequence in context: A224287 A248838 A052398 * A297204 A071088 A177533

Adjacent sequences: A047887 A047888 A047889 * A047891 A047892 A047893

KEYWORD

nonn,easy

AUTHOR

Eric Rains (rains(AT)caltech.edu), N. J. A. Sloane

EXTENSIONS

More terms from Naohiro Nomoto, Mar 01 2002

More terms from Alois P. Heinz, Apr 10 2012

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 10 02:09 EST 2022. Contains 358712 sequences. (Running on oeis4.)