cp's OEIS Frontend

A293374 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 and all ten letters occur at least once in the partition.

%I A293374 #8 Oct 11 2017 06:45:42
%S A293374 8879558,507478240,16328012830,386564408490,7585143426265,
%T A293374 129920818441752,2021599595359635,29144953777135120,
%U A293374 396700415630121560,5147755142273696760,64343348623810658670,779040642478793472040,9192718895981030349425,106097174229823135572590
%N A293374 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 and all ten letters occur at least once in the partition.
%H A293374 Alois P. Heinz, <a href="/A293374/b293374.txt">Table of n, a(n) for n = 10..1000</a>
%F A293374 a(n) ~ c * 10^n, where c = 3.1513858636401513585013047835048959202713435... - _Vaclav Kotesovec_, Oct 11 2017
%p A293374 b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A293374       b(n, i-1, k)+`if`(i>n, 0, b(n-i, i, k)*binomial(i+k-1, k-1))))
%p A293374     end:
%p A293374 a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k))(10):
%p A293374 seq(a(n), n=10..30);
%Y A293374 Column k=10 of A261719.
%K A293374 nonn
%O A293374 10,1
%A A293374 _Alois P. Heinz_, Oct 07 2017