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.

1, 1, 5, 30, 241, 2356, 27315, 364319, 5488468, 92040141, 1698933390, 34206221161, 745622368096, 17486274798203, 438859174516837, 11732964019785027, 332818604033186036, 9981540739647177238, 315518234680527952625, 10482878954868309043158, 365158449014981632341391

Offset: 0

Author

Alois P. Heinz, May 06 2015

Keywords

• nonn

Examples

			a(0) = 1: {}.
a(1) = 1: {a}.
a(2) = 5: {a,a}, {aa}, {ab}, {ba}, {a,b}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A257740, A319518.

Programs

Mathematica

A[n_, k_] := A[n, k] = If[n == 0, 1, Sum[DivisorSum[j, #*k^#&]*A[n - j, k], {j, 1, n}]/n];
T[n_, k_] := Sum[A[n, k - i]*(-1)^i*Binomial[k, i], {i, 0, k}];
a[n_] := Sum[T[n, k], {k, 0, n}];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Jun 01 2022, after Alois P. Heinz in A257740 *)

Formula

a(n) = Sum_{k=0..n} A257740(n,k).