OFFSET
0,3
FORMULA
a(n) = 2*binomial(n,2)*A000262(n-2).
E.g.f.: x^2*exp(x/(1-x)) = d/dy G(x,y)|y=1 where G(x,y) is the e.g.f. for A351823.
a(n) = Sum_{k=0..floor(n/2)} k * A351823(n,k).
a(n) ~ n^(n - 1/4) * exp(2*sqrt(n) - n - 1/2) / sqrt(2) * (1 - 101/(48*sqrt(n))). - Vaclav Kotesovec, Feb 21 2022
a(n) = 2 * A129652(n,2). - Alois P. Heinz, Feb 22 2022
Recurrence: (n-2)*a(n) = n*(2*n-5)*a(n-1) - (n-4)*(n-1)*n*a(n-2). - Vaclav Kotesovec, Mar 20 2023
MATHEMATICA
nn = 22; Range[0, nn]! CoefficientList[Series[D[Exp[ x/(1 - x) - x ^2 + y x^2], y] /. y -> 1, {x, 0, nn}], x]
Join[{0, 0, 2}, Table[n!*Hypergeometric1F1[n-1, 2, 1]/E, {n, 3, 25}]] (* Vaclav Kotesovec, Feb 21 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Feb 20 2022
STATUS
approved