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

%I #23 Apr 06 2017 13:09:41

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

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

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

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

%e a(0) = 1: the empty partition.

%e a(1) = 1: 1.

%e a(2) = 3: 22, 211, 1111.

%e 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.)

%Y Main diagonal of A213086.

%Y Cf. A000041, A206226, A284911.

%K nonn,more

%O 0,3

%A _Alois P. Heinz_, Apr 03 2017