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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.
4
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
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
Sequence in context: A144498 A201368 A072213 * A308946 A346681 A279155
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 06 2015
STATUS
approved