A293039 E.g.f.: exp(1 + x + x^2/2! + x^3/3! - exp(x)).

1, 0, 0, 0, -1, -1, -1, -1, 34, 125, 335, 791, -4027, -41328, -223510, -966174, -1082043, 22493107, 255137121, 1853859145, 8611832136, 6734302429, -364364045001, -4974309134233, -41550393316275, -223452696895652, -173393115915136, 14282249293678744

Offset: 0

Author

Seiichi Manyama, Sep 28 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..592

Crossrefs

Column k=3 of A293051.

Cf. A000587 (k=0), A293037 (k=1), A293038 (k=2), this sequence (k=3), A293040 (k=4).

Cf. A057837.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[Exp[1+x+x^2/2!+x^3/3!-Exp[x]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Oct 19 2022 *)

PARI

my(x='x+O('x^66)); Vec(serlaplace(exp(-exp(x)+1+x+x^2/2+x^3/6)))

Formula

a(0) = 1; a(n) = -Sum_{k=4..n} binomial(n-1,k-1) * a(n-k). - Ilya Gutkovskiy, Nov 20 2020