A378503 Expansion of (Sum_{k>=0} binomial(4*k,k) * x^k)^3.

1, 12, 132, 1396, 14436, 147120, 1483996, 14854968, 147821604, 1464031120, 14443875984, 142042418004, 1393053544508, 13630170286224, 133092301736232, 1297274743175856, 12624909478998948, 122692158505386960, 1190859983017752880, 11545524234978791952, 111820579340839270416

Offset: 0

Author

Seiichi Manyama, Nov 28 2024

Keywords

• nonn

Crossrefs

Cf. A005810, A078995, A337291, A378484.

Cf. A002457, A378483.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, binomial(4*k, k)*x^k)^3)

Formula

a(n) = Sum_{i+j+k=n, i,j,k >= 0} binomial(4*i,i) * binomial(4*j,j) * binomial(4*k,k).

G.f.: B(x)^3 where B(x) is the g.f. of A005810.

27*a(n) - 256*a(n-1) = 18*A005810(n) - A337291(n) for n > 0.