A333372 a(n) = prime(n)# - Sum_{k=1..n-1} prime(k)# * a(n-k), where prime()# = A002110.

1, 2, 2, 14, 110, 1526, 20858, 388718, 7614806, 183489830, 5561422394, 174355099682, 6611001621542, 274364327631194, 11859712864132730, 562348710109678226, 30121397642062848278, 1792060484721674304638, 109581661931207939415266, 7388364108380826136619810

Offset: 0

Author

Ilya Gutkovskiy, Mar 17 2020

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Primorial
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A000698, A002110, A003319, A030018, A167894, A307364.

Programs

Mathematica

primorial[n_] := Product[Prime[k], {k, 1, n}]; a[n_] := a[n] = primorial[n] - Sum[primorial[k] a[n - k], {k, 1, n - 1}]; Table[a[n], {n, 0, 19}]

Formula

G.f.: 2 - 1 / (Sum_{k>=0} prime(k)# * x^k).