A307364 Expansion of 1/(1 - Sum_{k>=1} prime(k)#*x^k), where prime(k)# is the product of first k primes (A002110).

1, 2, 10, 62, 454, 4310, 49954, 746078, 13180750, 283749638, 7747573666, 234558524690, 8437098259486, 340293472077722, 14523592739559970, 676119676949381762, 35425760935764788014, 2070535245695282709950, 125884029549845876309674, 8379955313909510350628018

Offset: 0

Author

Ilya Gutkovskiy, Apr 05 2019

Keywords

• nonn

Comments

Invert transform of A002110.

Crossrefs

Cf. A002110, A030017, A051296.

Programs

Mathematica

nmax = 19; CoefficientList[Series[1/(1 - Sum[Product[Prime[j], {j, k}] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[Product[Prime[j], {j, k}] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A002110(k)*a(n-k).