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%I #6 Oct 14 2017 10:51:47
%S 47293,2075948,53476920,1058754564,17866313444,270907452704,
%T 3807403790792,50592275219138,644225577441572,7936529529027736,
%U 95254972055989564,1119634204276346052,12939870424457764200,147501747088827091436,1662420626477581539972
%N Number of compositions 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 composition.
%H Alois P. Heinz, <a href="/A293584/b293584.txt">Table of n, a(n) for n = 7..975</a>
%F a(n) = 56*a(n-1) - 1400*a(n-2) + 20804*a(n-3) - 206864*a(n-4) + 1472576*a(n-5) - 7857468*a(n-6) + 32533654*a(n-7) - 107414264*a(n-8) + 288967984*a(n-9) - 644267912*a(n - 10) + 1206205784*a(n - 11) - 1915352424*a(n - 12) + 2598569764*a(n - 13) - 3027512680*a(n - 14) + 3038439672*a(n - 15) - 2630187744*a(n - 16) + 1962871608*a(n - 17) - 1260043528*a(n - 18) + 692851920*a(n - 19) - 324225312*a(n - 20) + 127932656*a(n - 21) - 42016752*a(n - 22) + 11279872*a(n - 23) - 2411968*a(n - 24) + 395168*a(n - 25) - 46592*a(n - 26) + 3520*a(n - 27) - 128*a(n - 28). - _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))(7):
%p seq(a(n), n=7..30);
%Y Column k=7 of A261781.
%K nonn
%O 7,1
%A _Alois P. Heinz_, Oct 12 2017
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