A362278 Expansion of e.g.f. exp(x - 3*x^2/2).

1, 1, -2, -8, 10, 106, -44, -1952, -1028, 45820, 73576, -1301024, -3729032, 43107832, 188540080, -1621988864, -10106292464, 67749173008, 583170088672, -3075285253760, -36315980308064, 148201134917536, 2436107894325568, -7345167010231808

Offset: 0

Author

Seiichi Manyama, Apr 13 2023

Keywords

• sign
• easy

Links

• Winston de Greef, Table of n, a(n) for n = 0..690

Crossrefs

Column k=3 of A362277.

Cf. A115327.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[Exp[x-3 x^2/2],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Apr 18 2023 *)

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-3*x^2/2)))

Formula

a(n) = a(n-1) - 3*(n-1)*a(n-2) for n > 1.

a(n) = n! * Sum_{k=0..floor(n/2)} (-3/2)^k / (k! * (n-2*k)!).