A293038 E.g.f.: exp(1 + x + x^2/2! - exp(x)).

1, 0, 0, -1, -1, -1, 9, 34, 90, -71, -1645, -9439, -25367, 45902, 1070146, 7122361, 24063637, -54352333, -1501032375, -12319959348, -53177369044, 80189626539, 3910291080509, 40317032441401, 228707685648269, 38882013140648, -16392939262378536

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=2 of A293051.

Cf. A000587 (k=0), A293037 (k=1), this sequence (k=2), A293039 (k=3), A293040 (k=4).

Cf. A006505.

Programs

Maple

seq(factorial(n) * coeftayl(exp(1+x+x^2/2!-exp(x)), x = 0, n),n = 0..50); # Muniru A Asiru, Oct 05 2017

PARI

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

Formula

a(0) = 1; a(n) = -Sum_{k=3..n} binomial(n-1,k-1) * a(n-k). - Ilya Gutkovskiy, Nov 20 2020