A293038 - OEIS

%I #21 Nov 21 2020 07:20:55

%S 1,0,0,-1,-1,-1,9,34,90,-71,-1645,-9439,-25367,45902,1070146,7122361,

%T 24063637,-54352333,-1501032375,-12319959348,-53177369044,80189626539,

%U 3910291080509,40317032441401,228707685648269,38882013140648,-16392939262378536

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

%H Seiichi Manyama, <a href="/A293038/b293038.txt">Table of n, a(n) for n = 0..592</a>

%F a(0) = 1; a(n) = -Sum_{k=3..n} binomial(n-1,k-1) * a(n-k). - _Ilya Gutkovskiy_, Nov 20 2020

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

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

%Y Column k=2 of A293051.

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

%Y Cf. A006505.

%K sign

%O 0,7

%A _Seiichi Manyama_, Sep 28 2017