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URL: https://oeis.org/A293809

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A293809
Number of multisets of exactly n nonempty words with a total of 2n letters over 2n-ary alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
2
1, 2, 7, 22, 73, 240, 818, 2824, 10004, 36252, 134594, 512632, 2002797, 8037634, 33122211, 140287074, 610344666, 2728599114, 12524559427, 59014996342, 285169596358, 1412357461074, 7161541766341, 37150562120334, 196945057245451, 1066104659977212
OFFSET
0,2
LINKS
FORMULA
G.f.: Product_{j>=1} 1/(1-x^j)^A000085(j+1).
Euler transform of j-> A000085(j+1).
a(n) = A293808(2n,n).
EXAMPLE
a(0) = 1: {}.
a(1) = 2: {aa}, {ab}.
a(2) = 7: {a,aaa}, {a,aab}, {a,aba}, {a,abc}, {aa,aa}, {aa,ab}, {ab,ab}.
MAPLE
g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
g(d+1), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..30);
MATHEMATICA
g[n_] := g[n] = If[n < 2, 1, g[n-1] + (n-1)*g[n-2]];
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d*g[d+1], {d, Divisors[j]}]*a[n-j], {j, 1, n}]/n];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Nov 23 2023, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A294010 A294011 A294012 * A307976 A114495 A389871
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 16 2017
STATUS
approved