A367877 Expansion of e.g.f. exp(x * (3 - 2*exp(x))).

1, 1, -3, -17, -7, 331, 1669, -2561, -82447, -411821, 1602941, 38344615, 209694121, -1133998085, -29424823819, -194721585329, 978185645537, 33795275629219, 290738927334637, -827164853506313, -53319390538573159, -621202281347942069, -249829452752930203

Offset: 0

Author

Seiichi Manyama, Dec 03 2023

Keywords

• sign
• easy

Crossrefs

Cf. A367876.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[Exp[x(3-2Exp[x])],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Apr 13 2025 *)

PARI

a(n) = sum(k=0, n, (-2)^k*(k+3)^(n-k)*binomial(n, k));

Formula

G.f.: Sum_{k>=0} (-2*x)^k / (1 - (k+3)*x)^(k+1).

a(n) = Sum_{k=0..n} (-2)^k * (k+3)^(n-k) * binomial(n,k).