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

0,3

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A257740, A319518.

Sequence in context: A144498 A201368 A072213 * A308946 A346681 A279155

Adjacent sequences: A257738 A257739 A257740 * A257742 A257743 A257744

Keyword

nonn

Author

Alois P. Heinz, May 06 2015

Status

approved