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

0,2

Links

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

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

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);

Crossrefs

Column k=9 of A261718.

Sequence in context: A064199 A092343 A261176 * A229283 A144073 A261801

Adjacent sequences: A261740 A261741 A261742 * A261744 A261745 A261746

Keyword

nonn

Author

Alois P. Heinz, Aug 30 2015

Status

approved