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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 and all nine letters occur at least once in the partition.
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%I #8 Oct 11 2017 06:45:08

%S 871030,41488902,1106315145,22148014950,366764207877,5369282570448,

%T 71433531608103,887892874465104,10433233718235522,117558189248146187,

%U 1278057588056171991,13515236446777067727,139538852470920866367,1413457490580676488090,14081562892529164704060

%N 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 and all nine letters occur at least once in the partition.

%H Alois P. Heinz, <a href="/A293373/b293373.txt">Table of n, a(n) for n = 9..1000</a>

%F a(n) ~ c * 9^n, where c = 3.23950351986835655716873222462341048089067679826... - _Vaclav Kotesovec_, Oct 11 2017

%p b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p b(n, i-1, k)+`if`(i>n, 0, b(n-i, i, k)*binomial(i+k-1, k-1))))

%p end:

%p a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k))(9):

%p seq(a(n), n=9..30);

%Y Column k=9 of A261719.

%K nonn

%O 9,1

%A _Alois P. Heinz_, Oct 07 2017