A378612 a(n) = Sum_{k=0..n} binomial(3*n+k-1,k) * binomial(n-1,n-k).

1, 3, 27, 264, 2703, 28443, 304740, 3306852, 36225519, 399755001, 4437142467, 49485052224, 554059164036, 6224177431332, 70120015345512, 791898021185484, 8962485528377583, 101626868754849381, 1154295872365035537, 13130360954151723480, 149562006735075309783

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

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

a(n) = (1/4)^n * [x^(3*n)] 3/(1 - x/(1 - x))^n for n > 0.

Prog

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

Crossrefs

Cf. A002002, A378611, A378613.

Cf. A369012.

Sequence in context: A279658 A370620 A373818 * A026294 A199688 A275998

Adjacent sequences: A378608 A378610 A378611 * A378613 A378614 A378626

Keyword

nonn,new

Author

Seiichi Manyama, Dec 01 2024

Status

approved