A361531 Expansion of e.g.f. exp(1 - exp(x) + x^3/6).
1, -1, 0, 2, -3, -2, 21, -44, -62, 631, -1367, -3170, 34849, -86855, -302964, 3058342, -8509971, -36488802, 430842051, -1111575888, -6244999438, 78663444549, -250850311489, -1724880111306, 18475299723737, -65061274823853, -444914618968648, 6831921081061986
Offset: 0
Programs
-
PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(1-exp(x)+x^3/6)))
Formula
a(0) = 1, a(1) = -1, a(2) = 0; a(n) = binomial(n-1,2) * a(n-3) - Sum_{k=1..n} binomial(n-1,k-1) * a(n-k).