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

0,2

Comments

a(100) is negative.

Links

Table of n, a(n) for n=0..25.

Formula

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

Prog

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

Crossrefs

Cf. A382536, A382649.

Sequence in context: A156832 A092780 A004282 * A374488 A216725 A334038

Adjacent sequences: A382647 A382648 A382649 * A382651 A382652 A382653

Keyword

sign,easy

Author

Seiichi Manyama, Apr 02 2025

Status

approved