OFFSET
1,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Rook Graph
Eric Weisstein's World of Mathematics, Total Dominating Set
FORMULA
a(n) = Sum_{k=0,..n} (-1)^k*binomial(n,k)^2*k!*(2*(n-k)^(n-k) - (n-k)!). - Andrew Howroyd, Apr 20 2018
a(n) ~ 2 * (exp(1) - 1)^(n + 1/2) * n^n / exp(n + 1/2). - Vaclav Kotesovec, Apr 20 2018
MATHEMATICA
Table[(-1)^n n! + Sum[(-1)^k Binomial[n, k]^2 k! (2 (n - k)^(n - k) - (n - k)!), {k, 0, n - 1}], {n, 20}]
2 Table[(-1)^n n! + Sum[(-1)^k Binomial[n, k]^2 k! (n - k)^(n - k), {k, 0, n - 1}], {n, 20}] (* Eric W. Weisstein, Jan 18 2019 *)
PROG
(PARI) a(n) = {sum(k=0, n, (-1)^k*binomial(n, k)^2*k!*(2*(n-k)^(n-k) - (n-k)!))} \\ Andrew Howroyd, Apr 20 2018
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Eric W. Weisstein, Apr 19 2018
EXTENSIONS
Terms a(6) and beyond from Andrew Howroyd, Apr 20 2018
STATUS
approved