A261744 Number of partitions of n where each part i is marked with a word of length i over a denary alphabet whose letters appear in alphabetical order.

1, 10, 155, 1770, 21440, 228502, 2544125, 26385600, 279082750, 2855995900, 29442232007, 298239664140, 3034263224145, 30563607210830, 308545853368510, 3098369166354518, 31146484546140435, 312188428888116430, 3131008962348253370, 31350509429122574890

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=10 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+9, 9))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..30);

Formula

a(n) ~ c * 10^n, where c = Product_{k>=2} 1/(1 - binomial(k+9,9)/10^k) = 3.1513858636401513585013047835048959202713435... - Vaclav Kotesovec, Oct 11 2017, updated May 10 2021

G.f.: Product_{k>=1} 1 / (1 - binomial(k+9,9)*x^k). - Ilya Gutkovskiy, May 10 2021