A261743 Number of partitions of n where each part i is marked with a word of length i over a nonary alphabet whose letters appear in alphabetical order.

1, 9, 126, 1299, 14211, 136611, 1373127, 12838293, 122478147, 1129559068, 10495764324, 95773104459, 877873080195, 7963150929030, 72400207009635, 654588661768353, 5924851016703093, 53460853371243261, 482688774419853026, 4350478100196378069, 39224153751141474936

Offset: 0

Author

Alois P. Heinz, Aug 30 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=9 of A261718.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1)+`if`(i>n, 0, b(n-i, i)*binomial(i+8, 8))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..30);

Formula

a(n) ~ c * 9^n, where c = Product_{k>=2} 1/(1 - binomial(k+8,8)/9^k) = 3.23950351986835655716873222462341048089067679826... - Vaclav Kotesovec, Oct 11 2017, updated May 10 2021

G.f.: Product_{k>=1} 1 / (1 - binomial(k+8,8)*x^k). - Ilya Gutkovskiy, May 10 2021