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

0,2

Links

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

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

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);

Crossrefs

Column k=10 of A261718.

Sequence in context: A061654 A298081 A240374 * A229284 A087603 A292837

Adjacent sequences: A261741 A261742 A261743 * A261745 A261746 A261747

Keyword

nonn

Author

Alois P. Heinz, Aug 30 2015

Status

approved