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A318113
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Number of compositions of n into exactly n nonnegative parts <= five.
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2
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1, 1, 3, 10, 35, 126, 456, 1667, 6147, 22825, 85228, 319683, 1203632, 4546270, 17218995, 65372310, 248705155, 947926359, 3618884895, 13836004764, 52968655260, 203022926480, 779008308235, 2992051471500, 11502445734096, 44256184906376, 170408995261326
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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^6-1)/(x-1))^n.
a(n) <= A088218(n) with equality only for n < 6.
a(n) = Sum_{k=0..floor(n/6)} (-1)^k * binomial(n,k) * binomial(2*n-6*k-1,n-6*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, 5))))
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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