A261783 Number of compositions of n where each part i is marked with a word of length i over an n-ary alphabet whose letters appear in alphabetical order.

1, 1, 7, 73, 1031, 18501, 403495, 10366833, 306717703, 10271072557, 384058268507, 15861842372465, 717135437119271, 35228475333207937, 1868440035684996207, 106412817671933423073, 6477200889282232394759, 419626639092214594301373, 28829330550533269570699411

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..365

Formula

a(n) = A261780(n,n).

a(n) = [x^n] (1-x)^n/(2*(1-x)^n-1).

a(n) ~ n^n / (sqrt(2) * (log(2))^(n+1)). - Vaclav Kotesovec, Sep 21 2019

Maple

A:= proc(n, k) option remember; `if`(n=0, 1,
      add(A(n-j, k)*binomial(j+k-1, k-1), j=1..n))
    end:
a:= n-> A(n$2):
seq(a(n), n=0..20);

Mathematica

A[n_, k_] := A[n, k] = If[n == 0, 1, Sum[A[n - j, k]*Binomial[j + k - 1, k - 1], {j, 1, n}]]; a[n_] := A[n, n]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 24 2017, translated from Maple *)

Crossrefs

Main diagonal of A261780.

Cf. A209668.

Sequence in context: A084363 A321837 A050352 * A250917 A112939 A058350

Adjacent sequences: A261780 A261781 A261782 * A261784 A261785 A261786

Keyword

nonn

Author

Alois P. Heinz, Aug 31 2015

Status

approved