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A371827
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a(n) = Sum_{k=0..floor(n/3)} n^k * binomial(2*n-2*k,n-3*k).
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3
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1, 2, 6, 23, 94, 392, 1680, 7387, 33110, 150905, 698996, 3287550, 15685420, 75877427, 371994692, 1847450970, 9290557158, 47291312897, 243574276884, 1268915237141, 6683909556420, 35585631836229, 191433293140656, 1040197718292138, 5707318227692796
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = [x^n] 1/((1-x-n*x^3) * (1-x)^n).
a(n) ~ exp(4*n^(2/3)/3 + 2*n^(1/3)/9) * n^(n/3) / 3. - Vaclav Kotesovec, Apr 07 2024
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MATHEMATICA
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Join[{1}, Table[Sum[n^k Binomial[2n-2k, n-3k], {k, 0, Floor[n/3]}], {n, 30}]] (* Harvey P. Dale, Aug 10 2024 *)
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PROG
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(PARI) a(n) = sum(k=0, n\3, n^k*binomial(2*n-2*k, n-3*k));
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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