A362161 Expansion of e.g.f. exp(-x * sqrt(1-4*x)).

1, -1, 5, -1, 121, 1039, 20221, 416975, 10573361, 309650399, 10335294901, 386839539679, 16045117551145, 730346985279599, 36191355037097261, 1939288174467052079, 111724538085236200801, 6886112439557645126335, 452112545350761238085221

Offset: 0

Author

Seiichi Manyama, Apr 10 2023

Keywords

• sign
• easy

Crossrefs

Cf. A362158.

Programs

PARI

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

Formula

a(n) = (-1)^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