A293040 E.g.f.: exp(1 + x + x^2/2! + x^3/3! + x^4/4! - exp(x)).

1, 0, 0, 0, 0, -1, -1, -1, -1, -1, 125, 461, 1253, 3002, 6720, -111684, -978758, -5246983, -22948029, -89534309, 164027151, 5722510249, 55413784239, 393256686307, 2377996545081, 7807749195198, -46231762188586, -1125536160278906, -12849721017510166

Offset: 0

Author

Seiichi Manyama, Sep 28 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..593

Crossrefs

Column k=4 of A293051.

Cf. A000587 (k=0), A293037 (k=1), A293038 (k=2), A293039 (k=3), this sequence (k=4).

Cf. A057814.

Programs

Maple

seq(factorial(n)*coeftayl(exp(1+x+x^2/2!+x^3/3!+x^4/4!-exp(x)), x = 0, n),n=0..50); # Muniru A Asiru, Oct 06 2017

PARI

my(x='x+O('x^66)); Vec(serlaplace(exp(-exp(x)+1+x+x^2/2+x^3/6+x^4/24)))

Formula

a(0) = 1; a(n) = -Sum_{k=5..n} binomial(n-1,k-1) * a(n-k). - Ilya Gutkovskiy, Nov 20 2020