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

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

Offset

0,3

Links

Table of n, a(n) for n=0..10.

Formula

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

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

Example

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.)

Crossrefs

Main diagonal of A213086.

Cf. A000041, A206226, A284911.

Sequence in context: A342966 A359976 A034234 * A081721 A013009 A301920

Adjacent sequences: A284642 A284643 A284644 * A284646 A284647 A284648

Keyword

nonn,more

Author

Alois P. Heinz, Apr 03 2017

Status

approved