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!)
A322439 Number of ordered pairs of integer partitions of n where no part of the first is greater than any part of the second. 7
1, 1, 3, 5, 11, 15, 33, 42, 82, 114, 195, 258, 466, 587, 954, 1317, 2021, 2637, 4124, 5298, 7995, 10565, 15075, 19665, 28798, 36773, 51509, 67501, 93060, 119299, 165589, 209967, 285535, 366488, 487536, 622509, 833998, 1048119, 1380410, 1754520, 2291406, 2876454 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = Sum_{k = 1...n} A026820(n, k) * A026794(n, k).

EXAMPLE

The a(5) = 15 pairs of integer partitions:

      (5)|(5)

     (41)|(5)

     (32)|(5)

    (311)|(5)

    (221)|(5)

    (221)|(32)

   (2111)|(5)

   (2111)|(32)

  (11111)|(5)

  (11111)|(41)

  (11111)|(32)

  (11111)|(311)

  (11111)|(221)

  (11111)|(2111)

  (11111)|(11111)

MAPLE

g:= proc(n, i) option remember; `if`(n=0 or i=1, 1,

      g(n, i-1) +g(n-i, min(i, n-i)))

    end:

b:= proc(n, i) option remember; `if`(n=0, 1,

      `if`(i>n, 0, b(n, i+1)+b(n-i, i)))

    end:

a:= proc(n) option remember; `if`(n=0, 1,

      add(g(n, i)*b(n-i, i), i=1..n))

    end:

seq(a(n), n=0..50);  # Alois P. Heinz, Dec 09 2018

MATHEMATICA

Table[Length[Select[Tuples[IntegerPartitions[n], 2], Max@@First[#]<=Min@@Last[#]&]], {n, 20}]

CROSSREFS

Cf. A026794, A026820, A265947, A285573, A317144, A318915, A322435, A322436, A322440, A322441, A322442.

Sequence in context: A092929 A138879 A318915 * A018313 A219039 A074820

Adjacent sequences:  A322436 A322437 A322438 * A322440 A322441 A322442

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 08 2018

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 May 29 20:42 EDT 2020. Contains 334710 sequences. (Running on oeis4.)