A206226 -id:A206226 - cp's OEIS frontend

A347585 Number of partitions of n^2 into n or more parts.

1, 1, 4, 25, 201, 1773, 16751, 165083, 1681341, 17562238, 187255089, 2030853040, 22344663465, 248900855994, 2802367768848, 31848644363490, 364960085991118, 4212964989100093, 48953036382441044, 572178690287957687, 6723501191850208483, 79388206896842420091

Offset: 0

Seiichi Manyama, Sep 08 2021

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..100

Cf. A058399, A072213, A161408, A206226, A206240.

a(n) = [x^(n^2)] Sum_{k>=n} x^k / Product_{j=1..k} (1 - x^j).
a(n) = A072213(n) + A206240(n) - A206226(n).
a(n) ~ exp(Pi*sqrt(2/3)*n) / (4*sqrt(3)*n^2). - Vaclav Kotesovec, Sep 14 2021

A284645 Number of partitions of n^2 that are the sum of n not necessarily distinct partitions of n.

Original entry on oeis.org

1, 1, 3, 10, 55, 266, 1974, 11418, 88671, 613756, 4884308

Offset: 0

Alois P. Heinz, Apr 03 2017

			a(0) = 1: the empty partition.
a(1) = 1: 1.
a(2) = 3: 22, 211, 1111.
a(3) = 10: 333, 3321, 32211, 33111, 222111, 321111, 2211111, 3111111, 21111111, 111111111. (Two of the A206226(3) = 12 partitions are not counted here: 3222, 22221.)

Main diagonal of A213086.

Cf. A000041, A206226, A284911.

a(n) = A213086(n,n).

a(n) <= binomial(A000041(n)+n-1,n) with equality only for n<4.

cp's OEIS Frontend

A347585 Number of partitions of n^2 into n or more parts.

Views

Author

Keywords

Links

Crossrefs