A378151 G.f. A(x) satisfies A(x) = 1 + (x * (1+x) * A(x))^3.

1, 0, 0, 1, 3, 3, 4, 18, 45, 72, 153, 450, 1066, 2172, 5142, 13381, 31752, 72333, 176475, 441909, 1065528, 2551465, 6292857, 15620439, 38229235, 93698523, 232545105, 578019090, 1430290512, 3548336724, 8851036863, 22092054588, 55093739760, 137681640450

Offset

0,5

Links

Table of n, a(n) for n=0..33.

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(3*k,n-3*k) * binomial(3*k,k)/(2*k+1).

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(3*k, n-3*k)*binomial(3*k, k)/(2*k+1));

Crossrefs

Cf. A000045, A256169, A378152.

Cf. A115055, A378153.

Sequence in context: A118114 A366555 A266067 * A300368 A306521 A300369

Adjacent sequences: A378148 A378149 A378150 * A378152 A378153 A378154

Keyword

nonn

Author

Seiichi Manyama, Nov 18 2024

Status

approved