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A252654 Number of multisets of nonempty words with a total of n letters over n-ary alphabet. 9
1, 1, 7, 64, 843, 13876, 276792, 6438797, 170938483, 5091463423, 167965714273, 6074571662270, 238837895468954, 10138497426332796, 461941179848628434, 22478593443737857695, 1163160397700757351363, 63760710281671647692688, 3690276585886363643056992 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..350

FORMULA

a(n) = [x^n] Product_{j>=1} 1/(1-x^j)^(n^j).

a(n) = n-th term of the Euler transform of the powers of n.

a(n) ~ n^(n-3/4) * exp(2*sqrt(n) - 1/2) / (2*sqrt(Pi)). - Vaclav Kotesovec, Mar 14 2015

a(n) = [x^n] exp(n*Sum_{k>=1} x^k/(k*(1 - n*x^k))). - Ilya Gutkovskiy, Nov 20 2018

EXAMPLE

a(2) = 7: {aa}, {ab}, {ba}, {bb}, {a,a}, {a,b}, {b,b}.

MAPLE

with(numtheory):

A:= proc(n, k) option remember; `if`(n=0, 1, add(add(

       d*k^d, d=divisors(j)) *A(n-j, k), j=1..n)/n)

    end:

a:= n-> A(n$2):

seq(a(n), n=0..25);

MATHEMATICA

A[n_, k_] := A[n, k] = If[n == 0, 1, Sum[Sum[d*k^d, {d, Divisors[j]}]*A[n - j, k], {j, 1, n}]/n];

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

Table[a[n], {n, 0, 25}] (* Jean-Fran├žois Alcover, Mar 21 2017, translated from Maple *)

CROSSREFS

Main diagonal of A144074.

Cf. A292805, A292873.

Sequence in context: A261500 A173516 A197785 * A197787 A024095 A274823

Adjacent sequences:  A252651 A252652 A252653 * A252655 A252656 A252657

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 19 2014

EXTENSIONS

New name from comment by Alois P. Heinz, Sep 21 2018

STATUS

approved

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Last modified May 31 22:45 EDT 2020. Contains 334756 sequences. (Running on oeis4.)