A371827 a(n) = Sum_{k=0..floor(n/3)} n^k * binomial(2*n-2*k,n-3*k).
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
Offset: 0
Keywords
Programs
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Mathematica
Join[{1},Table[Sum[n^k Binomial[2n-2k,n-3k],{k,0,Floor[n/3]}],{n,30}]] (* Harvey P. Dale, Aug 10 2024 *) -
PARI
a(n) = sum(k=0, n\3, n^k*binomial(2*n-2*k, n-3*k));
Formula
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