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A261801
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Number of 9-compositions of n: matrices with 9 rows of nonnegative integers with positive column sums and total element sum n.
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2
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1, 9, 126, 1704, 22986, 310086, 4183260, 56435004, 761346207, 10271072557, 138563678736, 1869317246556, 25218347263608, 340212470558832, 4589695110222504, 61918074814238448, 835316485437693186, 11268981358631127288, 152026139882340589466
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OFFSET
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0,2
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COMMENTS
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Also the number of compositions of n where each part i is marked with a word of length i over a nonary alphabet whose letters appear in alphabetical order.
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LINKS
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FORMULA
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G.f.: (1-x)^9/(2*(1-x)^9-1).
a(n) = Sum_{k>=0} (1/2)^(k+1) * binomial(n-1+9*k,n). - Seiichi Manyama, Aug 06 2024
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1,
add(a(n-j)*binomial(j+8, 8), j=1..n))
end:
seq(a(n), n=0..20);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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