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A368889
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a(n) = Sum_{k=0..floor(n/2)} n^(3*k) * binomial(n-k,k).
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2
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1, 1, 9, 55, 4289, 47376, 10358713, 162592977, 70065589761, 1419907258279, 1015035028009001, 25173466118539344, 26947505294538873409, 790057195504021692521, 1183327797361056503499225, 40027334070963910087734751, 79925496016112851520801796097
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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] 1/(1 - x - n^3*x^2).
a(n) ~ n^(3*n/2) if n is even and a(n) ~ n^((3*n-1)/2)/2 if n is odd. - Vaclav Kotesovec, Jan 09 2024
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MATHEMATICA
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Table[Hypergeometric2F1[1/2 - n/2, -n/2, -n, -4*n^3], {n, 0, 20}] (* Vaclav Kotesovec, Jan 09 2024 *)
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PROG
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(PARI) a(n) = sum(k=0, n\2, n^(3*k)*binomial(n-k, k));
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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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