A257742 Number of multisets of nonempty words with a total of 2n letters over n-ary alphabet such that all n letters occur at least once in the multiset.

1, 2, 49, 3334, 428653, 87804401, 26047147641, 10515038040403, 5527943088161719, 3662449762145471938, 2981185419002290273673, 2921408464370908053081409, 3389743512704136305019696050, 4593040689601644978081159072298, 7182956101782940369861692674495595

Offset: 0

Author

Alois P. Heinz, May 06 2015

Keywords

• nonn

Examples

			a(0) = 1: {}.
a(1) = 2: {aa}, {a,a}.
a(2) = 49: {aaab}, {aaba}, {aabb}, {abaa}, {abab}, {abba}, {abbb}, {baaa}, {baab}, {baba}, {babb}, {bbaa}, {bbab}, {bbba}, {a,aab}, {a,aba}, {a,abb}, {a,baa}, {a,bab}, {a,bba}, {a,bbb}, {aa,ab}, {aa,ba}, {aa,bb}, {aaa,b}, {aab,b}, {ab,ab}, {ab,ba}, {ab,bb}, {aba,b}, {abb,b}, {b,baa}, {b,bab}, {b,bba}, {ba,ba}, {ba,bb}, {a,a,ab}, {a,a,ba}, {a,a,bb}, {a,aa,b}, {a,ab,b}, {a,b,ba}, {a,b,bb}, {aa,b,b}, {ab,b,b}, {b,b,ba}, {a,a,a,b}, {a,a,b,b}, {a,b,b,b}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A257740, A319519.

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_] := T[2n, n]; Table[a[n], {n, 0, 15}]
(* Jean-François Alcover, May 10 2022, after Alois P. Heinz in A257740 *)

Formula

a(n) = A257740(2n,n).

Extensions

New name from Alois P. Heinz, Sep 21 2018