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A318115
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Number of compositions of n into exactly n nonnegative parts <= seven.
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2
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1, 1, 3, 10, 35, 126, 462, 1716, 6427, 24229, 91828, 349570, 1335698, 5119856, 19678452, 75814560, 292695291, 1132074847, 4385740683, 17015510820, 66102536360, 257103599280, 1001078753370, 3901733646660, 15220908863866, 59427261280126, 232201593611796
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = [x^n] ((x^8-1)/(x-1))^n.
a(n) <= A088218(n) with equality only for n < 8.
a(n) = Sum_{k=0..floor(n/8)} (-1)^k * binomial(n,k) * binomial(2*n-8*k-1,n-8*k). - Ilya Gutkovskiy, Nov 03 2021
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0, 1,
`if`(i=0, 0, add(b(n-j, i-1), j=0..min(n, 7))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..30);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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