A362279 Expansion of e.g.f. exp(x - 5*x^2/2).

1, 1, -4, -14, 46, 326, -824, -10604, 18236, 442396, -378224, -22498024, -1695704, 1348185736, 1458406496, -92914595024, -202295082224, 7230872519696, 24425954508736, -626352572263904, -2946818250593824, 59688438975796576, 369104355288148096

Offset: 0

Author

Seiichi Manyama, Apr 13 2023

Keywords

• sign
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..649

Crossrefs

Column k=5 of A362277.

Cf. A115331.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-5*x^2/2)))

Formula

a(n) = a(n-1) - 5*(n-1)*a(n-2) for n > 1.

a(n) = n! * Sum_{k=0..floor(n/2)} (-5/2)^k / (k! * (n-2*k)!).