OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
a(n) = Sum_{k=0..n} t(k), where t = A000670 (ordered Bell numbers).
G.f. = A(x)/(1-x), where A(x) = g.f. for A000670 (see that entry). - N. J. A. Sloane, Apr 12 2014
a(n) ~ n! / (2* (log(2))^(n+1)). - Vaclav Kotesovec, Nov 08 2014
MATHEMATICA
t[n_] := Sum[StirlingS2[n, k]k!, {k, 0, n}]; Table[Sum[t[k], {k, 0, n}], {n, 0, 100}]
(* second program: *)
Fubini[n_, r_] := Sum[k!*Sum[(-1)^(i+k+r)(i+r)^(n-r)/(i!*(k-i-r)!), {i, 0, k-r}], {k, r, n}]; Fubini[0, 1] = 1; Table[Fubini[n, 1], {n, 0, 20}] // Accumulate (* Jean-François Alcover, Mar 31 2016 *)
PROG
(Maxima)
t(n):=sum(stirling2(n, k)*k!, k, 0, n);
makelist(sum(t(k), k, 0, n), n, 0, 40);
(Magma)
A000670:=func<n | &+[StirlingSecond(n, i)*Factorial(i): i in [0..n]]>;
[&+[A000670(k): k in [0..n]]: n in [0..19]]; // Bruno Berselli, Oct 03 2012
(PARI) for(n=0, 30, print1(sum(k=0, n, sum(j=0, k, j!*stirling(k, j, 2))), ", ")) \\ G. C. Greubel, Feb 07 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Emanuele Munarini, Oct 02 2012
STATUS
approved