OFFSET
0,3
COMMENTS
By analogy with subfactorials, which are the inverse binomial transform of the factorials.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..350
FORMULA
a(n) = Sum_{k=0..n} (-1)^(n-k) C(n,k) Prime(k)#, where p# is p primorial and Prime(0)# = 1.
EXAMPLE
a(3) = 30 - 3*6 + 3*2 - 1 = 17.
MAPLE
b:= proc(n) option remember; `if`(n=0, 1, ithprime(n)*b(n-1)) end:
a:= n-> add(binomial(n, k)*b(k)*(-1)^(n-k), k=0..n):
seq(a(n), n=0..20); # Alois P. Heinz, Sep 19 2016
MATHEMATICA
b[n_] := b[n] = If[n==0, 1, Prime[n]*b[n-1]]; a[n_] := Sum[Binomial[n, k]* b[k]*(-1)^(n-k), {k, 0, n}]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Mar 13 2017, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Franklin T. Adams-Watters, Aug 08 2006
EXTENSIONS
More terms from R. J. Mathar, Sep 18 2007
Edited by N. J. A. Sloane, May 15 2008 at the suggestion of R. J. Mathar
STATUS
approved