OFFSET
0,5
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..450
G. V. Milovanovich and A. Petojevich, Generalized Factorial Functions, Numbers and Polynomials, Math. Balkanica, Vol. 16 (2002), Fasc. 1-4.
FORMULA
From G. C. Greubel, Sep 13 2018: (Start)
a(n) = Sum_{j=0..(n-1)} Sum_{m=0..(j-1)} !m, where !n = Sum_{k=0..(n-1)} k! = A003422(n).
a(n) = ((n^2 -3*n +1) * !n - (n-2)*n! + 2*(n-1))/2.
a(n) = Sum_{j=0..(n-1)} ((j-1) * !j - j! + 1) = Sum_{j=0..(n-1)} A014144(n). (End)
MATHEMATICA
With S[n_]:= Sum[k!, {k, 0, n-1}];
Table[Sum[Sum[S[j], {j, 0, m-1}], {m, 0, n -1}], {n, 0, 30}] (* or *) Table[((n^2 - 3*n + 1)*S[n] - (n - 2)*n! + 2*(n - 1))/2, {n, 0, 30}] (* G. C. Greubel, Sep 13 2018 *)
PROG
(PARI) for(n=0, 30, print1(((n^2-3*n+1)*sum(k=0, n-1, k!) - (n-2)*n! + 2*(n -1))/2, ", ")) \\ G. C. Greubel, Sep 13 2018
(Magma) [0] cat [((n^2 -3*n +1)*(&+[Factorial(k): k in [0..(n-1)]]) -(n-2)*Factorial(n) +2*(n-1))/2: n in [1..30]]; // G. C. Greubel, Sep 13 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Dec 10 2008
EXTENSIONS
Prepended zeros and changed offset by G. C. Greubel, Sep 13 2018
STATUS
approved