OFFSET
0,3
COMMENTS
This sequence is the Akiyama-Tanigawa transform of the factorial numbers. - Peter Luschny, Apr 19 2024
FORMULA
a(n) = (-1)^n * Sum_{k=0..n} A163626(n, k)*k!. - Philippe Deléham, May 25 2015
a(n) ~ exp(-1/2) * n!^2. - Vaclav Kotesovec, Jul 05 2021
MAPLE
ATFactorial := proc(len)
local k, j, A, R, F; F := 1;
for k from 0 to len do
R[k] := F; F := F * (k + 1);
for j from k by -1 to 1 do
R[j - 1] := j * (R[j] - R[j-1])
od;
A[k] := R[0];
od; convert(A, list) end:
ATFactorial(17); # Peter Luschny, Apr 19 2024
MATHEMATICA
Table[Sum[StirlingS2[n+1, k+1](-1)^(n-k)k!^2, {k, 0, n}], {n, 0, 100}]
PROG
(Maxima) makelist(sum(stirling2(n+1, k+1)*(-1)^(n-k)*k!^2, k, 0, n), n, 0, 24);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emanuele Munarini, Jul 04 2011
STATUS
approved