A382650 Expansion of 1/(1 - x*(1 + 4*x)^(3/2))^3.

1, 3, 24, 100, 471, 2043, 8422, 34818, 137649, 543655, 2096508, 8031948, 30355155, 113929497, 423562614, 1565841650, 5745557853, 20989365057, 76206968356, 275721399480, 992423144247, 3562075121911, 12728422443654, 45379998032202, 161158522838105, 571293893581389

Offset: 0

Author

Seiichi Manyama, Apr 02 2025

Keywords

• sign
• easy

Comments

a(100) is negative.

Crossrefs

Cf. A382536, A382649.

Programs

PARI

a(n) = sum(k=0, n, 4^(n-k)*binomial(k+2, 2)*binomial(3*k/2, n-k));

Formula

a(n) = Sum_{k=0..n} 4^(n-k) * binomial(k+2,2) * binomial(3*k/2,n-k).