A378552 a(n) = Sum_{k=0..n} 9^k * binomial(n/3+k-1,k) * binomial(n-1,n-k).

1, 3, 51, 900, 16455, 307833, 5850000, 112445112, 2180050215, 42552000000, 835075676361, 16461248223588, 325696500000000, 6464447754891285, 128654307202482420, 2566472490000000000, 51302899404879842343, 1027391467409893403745, 20607804108000000000000

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = [x^n] 1/(1 - 9*x/(1-x))^(n/3).

Mathematica

a[n_]:=SeriesCoefficient[1/(1 - 9*x/(1-x))^(n/3), {x, 0, n}]; Array[a, 19, 0] (* Stefano Spezia, Nov 30 2024 *)

Prog

(PARI) a(n) = sum(k=0, n, 9^k*binomial(n/3+k-1, k)*binomial(n-1, n-k));

Crossrefs

Cf. A002002, A378551.

Cf. A372110.

Sequence in context: A248341 A145242 A182512 * A075869 A361051 A307369

Adjacent sequences: A378549 A378550 A378551 * A378553 A378554 A378555

Keyword

nonn

Author

Seiichi Manyama, Nov 30 2024

Status

approved