A362158 Expansion of e.g.f. -exp(x * sqrt(1-4*x)).

-1, -1, 3, 23, 119, 1119, 19259, 417143, 10567983, 309715199, 10335277619, 386840046999, 16045111426343, 730346987476703, 36191354975508459, 1939288175212058999, 111724538084900577119, 6886112439566787983103, 452112545350650426838883

Offset: 0

Author

Seiichi Manyama, Apr 10 2023

Keywords

• sign
• easy

Crossrefs

Cf. A362156.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(-exp(x*sqrt(1-4*x))))

Formula

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

a(n) ~ 2^(2*n - 5/2) * n^(n-1) / exp(n). - Vaclav Kotesovec, Apr 10 2023