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%I #6 Oct 14 2017 10:52:00
%S 4683,155928,3116220,48697048,657516672,8065687344,92540869002,
%T 1011476639976,10662168594984,109327852591208,1097238662684028,
%U 10827944900524680,105430826499237004,1015590292306277376,9698300806656595584,91961212434214073824,866974686508851897168
%N Number of compositions of n where each part i is marked with a word of length i over a senary alphabet whose letters appear in alphabetical order and all six letters occur at least once in the composition.
%H Alois P. Heinz, <a href="/A293583/b293583.txt">Table of n, a(n) for n = 6..1000</a>
%F a(n) = 42*a(n-1) - 770*a(n-2) + 8190*a(n-3) - 56854*a(n-4) + 275758*a(n-5) - 980010*a(n-6) + 2645668*a(n-7) - 5576808*a(n-8) + 9366788*a(n-9) - 12715312*a(n - 10) + 14078260*a(n - 11) - 12772248*a(n - 12) + 9499064*a(n - 13) - 5769584*a(n - 14) + 2837496*a(n - 15) - 1113568*a(n - 16) + 340784*a(n - 17) - 78416*a(n - 18) + 12768*a(n - 19) - 1312*a(n - 20) + 64*a(n - 21). - _Vaclav Kotesovec_, Oct 14 2017
%p b:= proc(n, k) option remember; `if`(n=0, 1,
%p add(b(n-j, k)*binomial(j+k-1, k-1), j=1..n))
%p end:
%p a:= n-> (k->add(b(n, k-i)*(-1)^i*binomial(k, i), i=0..k))(6):
%p seq(a(n), n=6..30);
%Y Column k=6 of A261781.
%K nonn
%O 6,1
%A _Alois P. Heinz_, Oct 12 2017
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