login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A067228 Number of rectangular standard Young tableaux with n cells. 3
1, 2, 2, 4, 2, 12, 2, 30, 44, 86, 2, 1190, 2, 860, 12014, 26886, 2, 184758, 2, 3359202, 2771342, 117574, 2, 327618902, 701149022, 1485802, 828630662, 27350160662, 2, 808310933492, 2, 2979826568702, 291724349282, 259289582, 557214344578322, 2031957220875002, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Number of ways to arrange the numbers 1, 2, .., n=i*j into an i*j rectangle so that each row and each column is increasing.

a(p) = 2 for prime p. - Alois P. Heinz, Jul 25 2012

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..350

FORMULA

a(n) = n! * Sum_{i|n} Product_{k=0..n/i-1} k!/(i+k)!. - Alois P. Heinz, Jul 25 2012

MAPLE

with(numtheory):

a:= n-> n! * add(mul(k!/(i+k)!, k=0..(n/i)-1), i=divisors(n)):

seq(a(n), n=1..40);  # Alois P. Heinz, Jul 25 2012

MATHEMATICA

a[n_] := n! * Sum[Product[k!/(i+k)!, {k, 0, n/i-1}], {i, Divisors[n]}]; Table[a[n], {n, 1, 40}] (* Jean-Fran├žois Alcover, Jul 02 2015, after Alois P. Heinz *)

CROSSREFS

Cf. A000085, A060854, A067231.

Column k=0 of A238707.

Sequence in context: A296071 A319342 A318834 * A332002 A229756 A227450

Adjacent sequences:  A067225 A067226 A067227 * A067229 A067230 A067231

KEYWORD

easy,nonn

AUTHOR

Naohiro Nomoto, Feb 20 2002

EXTENSIONS

Better name from Joerg Arndt, Feb 24 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 27 10:28 EDT 2021. Contains 347689 sequences. (Running on oeis4.)