A333048 - OEIS

%I #13 Mar 06 2020 15:28:12

%S 1,1,6,20,96,572,3971,31201,272334,2605268,27042522,302171806,

%T 3611295430,45911641817,618074912240,8776287336812,130994094465946,

%U 2049114914257540,33504826964461451,571285301051283841,10136481840545237652,186803012671904648805

%N Number of compositions of n^2 into powers of n.

%H Alois P. Heinz, <a href="/A333048/b333048.txt">Table of n, a(n) for n = 0..400</a>

%F a(n) = 1 + Sum_{j=0..n} binomial(n*(n-j)+j,j) if n>1, a(0) = a(1) = 1.

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

%e a(1) = 1: 1.

%e a(2) = 6: 1111, 112, 121, 211, 22, 4.

%e a(3) = 20: 111111111, 1111113, 1111131, 1111311, 1113111, 1131111, 1311111, 3111111, 11133, 11313, 11331, 13113, 13131, 13311, 31113, 31131, 31311, 33111, 333, 9.

%p a:= n-> `if`(n<2, 1, 1+add(binomial(n*(n-j)+j, j), j=0..n)):

%p seq(a(n), n=0..21);

%Y Cf. A000290, A011782, A103488, A332721, A332747, A332796.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Mar 06 2020