OFFSET
0,2
LINKS
FORMULA
Binomial transform of primorial numbers, A002110.
EXAMPLE
a(3) = 55 = (1, 3, 3, 1) dot (1, 2, 6, 30) = (1 + 6 + 18 + 30), where A002110 = (1, 2, 6, 30, 210, 2310, ...).
MAPLE
b:= proc(n) option remember; `if`(n=0, 1, ithprime(n)*b(n-1)) end:
a:= n-> add(binomial(n, k)*b(k), k=0..n):
seq(a(n), n=0..20); # Alois P. Heinz, Sep 20 2016
MATHEMATICA
b[n_] := b[n] = If[n==0, 1, Prime[n]*b[n-1]]; a[n_] := Sum[Binomial[n, k]*b[k], {k, 0, n}]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 22 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Dec 14 2007
EXTENSIONS
A few more terms from L. Edson Jeffery, Apr 11 2011
Explicit binomial sum formula added to the name by Antti Karttunen, Sep 19 2016
STATUS
approved