cp's OEIS Frontend

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.

%I A261744 #11 May 10 2021 06:24:46
%S A261744 1,10,155,1770,21440,228502,2544125,26385600,279082750,2855995900,
%T A261744 29442232007,298239664140,3034263224145,30563607210830,
%U A261744 308545853368510,3098369166354518,31146484546140435,312188428888116430,3131008962348253370,31350509429122574890
%N 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.
%H A261744 Alois P. Heinz, <a href="/A261744/b261744.txt">Table of n, a(n) for n = 0..1000</a>
%F A261744 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
%F A261744 G.f.: Product_{k>=1} 1 / (1 - binomial(k+9,9)*x^k). - _Ilya Gutkovskiy_, May 10 2021
%p A261744 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A261744       b(n, i-1)+`if`(i>n, 0, b(n-i, i)*binomial(i+9, 9))))
%p A261744     end:
%p A261744 a:= n-> b(n$2):
%p A261744 seq(a(n), n=0..30);
%Y A261744 Column k=10 of A261718.
%K A261744 nonn
%O A261744 0,2
%A A261744 _Alois P. Heinz_, Aug 30 2015