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A292805 Number of sets of nonempty words with a total of n letters over n-ary alphabet. 8
1, 1, 5, 55, 729, 12376, 250735, 5904746, 158210353, 4747112731, 157545928646, 5726207734545, 226093266070501, 9632339536696943, 440262935648935344, 21482974431740480311, 1114363790702406540897, 61219233429920494716931, 3550130647865299090804375 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..381

FORMULA

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

a(n) ~ n^(n - 3/4) * exp(2*sqrt(n) - 1/2) / (2*sqrt(Pi)). - Vaclav Kotesovec, Aug 26 2019

EXAMPLE

a(0) = 1: {}.

a(1) = 1: {a}.

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

MAPLE

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

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

    end:

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

seq(a(n), n=0..20);

MATHEMATICA

h[n_, i_, k_] := h[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[h[n - i*j, i - 1, k]*Binomial[k^i, j], {j, 0, n/i}]]];

a[n_] := h[n, n, n];

Table[a[n], {n, 0, 20}] (* Jean-Fran├žois Alcover, Jun 04 2018, from Maple *)

CROSSREFS

Main diagonal of A292804.

Cf. A252654, A292845.

Sequence in context: A114909 A038261 A246153 * A112019 A131846 A144577

Adjacent sequences:  A292802 A292803 A292804 * A292806 A292807 A292808

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 23 2017

STATUS

approved

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Last modified June 5 23:10 EDT 2020. Contains 334858 sequences. (Running on oeis4.)