cp's OEIS Frontend

A257741 Number of multisets of nonempty words with a total of n letters over n-ary alphabet such that if a letter occurs in the multiset all predecessors occur at least once.

%I A257741 #14 Jun 01 2022 14:44:59
%S A257741 1,1,5,30,241,2356,27315,364319,5488468,92040141,1698933390,
%T A257741 34206221161,745622368096,17486274798203,438859174516837,
%U A257741 11732964019785027,332818604033186036,9981540739647177238,315518234680527952625,10482878954868309043158,365158449014981632341391
%N A257741 Number of multisets of nonempty words with a total of n letters over n-ary alphabet such that if a letter occurs in the multiset all predecessors occur at least once.
%H A257741 Alois P. Heinz, <a href="/A257741/b257741.txt">Table of n, a(n) for n = 0..400</a>
%F A257741 a(n) = Sum_{k=0..n} A257740(n,k).
%e A257741 a(0) = 1: {}.
%e A257741 a(1) = 1: {a}.
%e A257741 a(2) = 5: {a,a}, {aa}, {ab}, {ba}, {a,b}.
%t A257741 A[n_, k_] := A[n, k] = If[n == 0, 1, Sum[DivisorSum[j, #*k^#&]*A[n - j, k], {j, 1, n}]/n];
%t A257741 T[n_, k_] := Sum[A[n, k - i]*(-1)^i*Binomial[k, i], {i, 0, k}];
%t A257741 a[n_] := Sum[T[n, k], {k, 0, n}];
%t A257741 Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Jun 01 2022, after _Alois P. Heinz_ in A257740 *)
%Y A257741 Cf. A257740, A319518.
%K A257741 nonn
%O A257741 0,3
%A A257741 _Alois P. Heinz_, May 06 2015