A337989 - OEIS

%I #5 Oct 09 2020 05:18:01

%S 1,2,120,131204813713122

%N Number of compositions (ordered partitions) of n^n into n-th powers.

%C The next term is too large to include.

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

%F a(n) = [x^(n^n)] 1 / (1 - Sum_{k>=1} x^(k^n)).

%e a(3) = 120 because 3^3 = 27 and we have [27], [8, 8, 8, 1, 1, 1] (20 permutations), [8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] (78 permutations), [8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] (20 permutations), [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] and 1 + 20 + 78 + 20 + 1 = 120.

%t Table[SeriesCoefficient[1/(1 - Sum[x^(k^n), {k, 1, n}]), {x, 0, n^n}], {n, 1, 4}]

%Y Cf. A011782, A224366, A290247, A331402.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Oct 06 2020