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A292796 Number of sets of nonempty words with a total of n letters over n-ary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter. 4
1, 1, 3, 13, 60, 326, 2065, 14508, 116845, 1039459, 10339365, 112376487, 1339665295, 17256611005, 240193792120, 3578746993871, 56986570945387, 963868021665359, 17281651020455445, 327058650473873893, 6519981694119182165, 136489249161324882063 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..450

FORMULA

a(n) = [x^n] Product_{j=1..n} (1+x^j)^A226873(j,n).

a(n) = A292795(n,n).

a(n) ~ c * n!, where c = A247551 = 2.529477472079152648... - Vaclav Kotesovec, Sep 28 2017

EXAMPLE

a(0) = 1: {}.

a(1) = 1: {a}.

a(2) = 3: {aa}, {ab}, {ba}.

a(3) = 13: {aaa}, {aab}, {aba}, {baa}, {abc}, {acb}, {bac}, {bca}, {cab}, {cba}, {aa,a}, {ab,a}, {ba,a}.

MAPLE

b:= proc(n, i, t) option remember; `if`(t=1, 1/n!,

      add(b(n-j, j, t-1)/j!, j=i..n/t))

    end:

g:= (n, k)-> `if`(k=0, `if`(n=0, 1, 0), n!*b(n, 0, k)):

h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,

      add(h(n-i*j, i-1, k)*binomial(g(i, k), j), j=0..n/i)))

    end:

a:= n-> h(n$3):

seq(a(n), n=0..30);

CROSSREFS

Main diagonal of A292795.

Row sums of A319498.

Cf. A226873, A292713.

Sequence in context: A074437 A026578 A199641 * A020007 A112731 A106884

Adjacent sequences:  A292793 A292794 A292795 * A292797 A292798 A292799

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 23 2017

STATUS

approved

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Last modified March 30 10:09 EDT 2020. Contains 333125 sequences. (Running on oeis4.)