OFFSET
1,3
LINKS
Eric Weisstein's World of Mathematics, Minimum Vertex Coloring.
Eric Weisstein's World of Mathematics, Path Complement Graph.
FORMULA
a(n) = (n+1)/2*((n+1)/2)! for n odd.
a(n) = (n/2)! for n even.
E.g.f.: (2*(6*x + x^3) + exp(x^2/4)*sqrt(Pi)*(4 + x*(8 + 8*x + x^3))*erf(x/2))/16. - Stefano Spezia, Mar 15 2024
D-finite with recurrence +2*(-29*n+56)*a(n) +2*(9*n-79)*a(n-1) +(29*n^2+31*n-52)*a(n-2) -(n-1)*(9*n-52)*a(n-3)=0. - R. J. Mathar, Mar 25 2024
MAPLE
A371210 := proc(n)
if type(n, 'odd') then
(n+1)/2*factorial((n+1)/2) ;
else
factorial(n/2) ;
end if;
end proc:
seq(A371210(n), n=1..40) ; # R. J. Mathar, Mar 25 2024
MATHEMATICA
Table[Piecewise[{{(n + 1)/2 ((n + 1)/2)!, Mod[n, 2] == 1}}, (n/2)!], {n, 31}]
CoefficientList[Series[(2 (6 x + x^3) + Exp[x^2/4] Sqrt[Pi] (4 + x (8 + 8 x + x^3)) Erf[x/2])/16, {x, 0, 20}], x] Range[0, 20]!
PROG
(Python)
from math import factorial
def A371210(n): return (m:=n+1>>1)*factorial(m) if n&1 else factorial(n>>1) # Chai Wah Wu, Mar 15 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Mar 15 2024
STATUS
approved