OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..350
Eric Weisstein's World of Mathematics, Primorial
FORMULA
E.g.f.: (Sum_{k>=0} prime(k)# * x^k / k!)^2, where prime()# = A002110.
a(n) = Sum_{k=0..n} binomial(n,k) * prime(k)# * prime(n-k)#.
MAPLE
p:= proc(n) option remember; `if`(n<1, 1, ithprime(n)*p(n-1)) end:
a:= n-> add(p(i)*p(n-i)*binomial(n, i), i=0..n):
seq(a(n), n=0..20); # Alois P. Heinz, Mar 17 2020
MATHEMATICA
primorial[n_] := Product[Prime[k], {k, 1, n}]; a[n_] := Sum[Binomial[n, k] primorial[k] primorial[n - k], {k, 0, n}]; Table[a[n], {n, 0, 18}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 17 2020
STATUS
approved