OFFSET
0,3
COMMENTS
Exponential convolution of factorials (A000142) and squares (A000290). - Vladimir Reshetnikov, Oct 07 2016
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..449
FORMULA
a(n) = A019461(2n).
For n>=2, a(n) = floor(2*e*n! - n - 2). - Benoit Cloitre, Feb 16 2003
a(n) = sum_{k=0...n} (n! / k!) * k^2. - Ross La Haye, Sep 21 2004
E.g.f.: x*(1+x)*exp(x)/(1-x). - Vladeta Jovovic, Dec 01 2004
MAPLE
f := proc(n) options remember; if n <= 1 then n elif n = 2 then 6 else -n*(n-2)*f(n-3)+(n-3)*n*f(n-2)+3*n*f(n-1)/(n-1); fi; end;
MATHEMATICA
a=0; lst={a}; Do[a=(a+n)*n; AppendTo[lst, a], {n, 2*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 14 2008 *)
RecurrenceTable[{a[0]==0, a[n]==n(n+a[n-1])}, a[n], {n, 20}] (* Harvey P. Dale, Oct 22 2011 *)
Round@Table[(2 E Gamma[n, 1] - 1) n, {n, 0, 20}] (* Round is equivalent to FullSimplify here, but is much faster - Vladimir Reshetnikov, Oct 07 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, "Urkonsaud_admin" (miti(AT)tula.sitek.net)
EXTENSIONS
Better description from Henry Bottomley, May 15 2000
STATUS
approved