A362163 Expansion of e.g.f. -exp(x * sqrt(1-2*x)).

-1, -1, 1, 8, 23, 64, 479, 6026, 80863, 1194488, 19951919, 374005774, 7768598111, 177019006748, 4389955280983, 117700126685714, 3392361648663359, 104592876994535056, 3434908279968850463, 119702402510430502358, 4411764405014665620799

Offset: 0

Author

Seiichi Manyama, Apr 10 2023

Keywords

• sign
• easy

Crossrefs

Cf. A362158, A362176.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(-exp(x*sqrt(1-2*x))))

Formula

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