OFFSET
0,3
FORMULA
E.g.f.: x*exp(x*(x+1)).
Recurrence: (n-1)*a(n) = n*a(n-1) + 2*(n-1)*n*a(n-2).
a(n) ~ 2^(n/2 - 1) * n^((n+1)/2) * exp(sqrt(n/2) - n/2 - 1/8).
MATHEMATICA
Table[n!*Sum[Binomial[i, n - 1 - i]/i!, {i, 0, n - 1}], {n, 0, 30}]
CoefficientList[Series[x*E^(x*(x+1)), {x, 0, 20}], x] * Range[0, 20]!
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 28 2017
STATUS
approved