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%I #8 Oct 11 2017 06:43:53
%S 11481,352793,6170486,83317577,941895458,9595504513,89629486436,
%T 792794568624,6679198773576,54486400898447,431529096734274,
%U 3349089312506511,25507319202685313,191694475039884663,1422950411887109983,10467534744471771547,76364568808571920303
%N Number of partitions of n where each part i is marked with a word of length i over a septenary alphabet whose letters appear in alphabetical order and all seven letters occur at least once in the partition.
%H Alois P. Heinz, <a href="/A293371/b293371.txt">Table of n, a(n) for n = 7..1000</a>
%F a(n) ~ c * 7^n, where c = 3.519268129363442517546929108933080435102442778133731795486515352... - _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))(7):
%p seq(a(n), n=7..30);
%Y Column k=7 of A261719.
%K nonn
%O 7,1
%A _Alois P. Heinz_, Oct 07 2017
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