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

0,2

Links

Table of n, a(n) for n=0..24.

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

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 *)

Prog

(PARI) a(n) = sum(k=0, n\3, n^k*binomial(2*n-2*k, n-3*k));

Crossrefs

Cf. A371825, A371826.

Cf. A368891.

Sequence in context: A191721 A150293 A370285 * A150294 A150295 A150296

Adjacent sequences: A371824 A371825 A371826 * A371828 A371829 A371830

Keyword

nonn

Author

Seiichi Manyama, Apr 07 2024

Status

approved