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A368893
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a(n) = Sum_{k=0..floor(n/3)} n^(n-2*k) * binomial(n-2*k,k).
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2
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1, 1, 4, 30, 288, 3500, 51876, 908607, 18374656, 421492491, 10815040000, 306944040931, 9547373318400, 322972830958648, 11805432990665664, 463673398064821875, 19474259980847153152, 870954834559130974358, 41323803842611198131264
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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 - n*x - n*x^3).
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MATHEMATICA
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Join[{1}, Table[n^n * HypergeometricPFQ[{1/3 - n/3, 2/3 - n/3, -n/3}, {1/2 - n/2, -n/2}, -27/(4*n^2)], {n, 1, 20}]] (* Vaclav Kotesovec, Jan 09 2024 *)
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PROG
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(PARI) a(n) = sum(k=0, n\3, n^(n-2*k)*binomial(n-2*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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