A307364 - OEIS

%I #5 Apr 05 2019 17:46:39

%S 1,2,10,62,454,4310,49954,746078,13180750,283749638,7747573666,

%T 234558524690,8437098259486,340293472077722,14523592739559970,

%U 676119676949381762,35425760935764788014,2070535245695282709950,125884029549845876309674,8379955313909510350628018

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

%C Invert transform of A002110.

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

%t nmax = 19; CoefficientList[Series[1/(1 - Sum[Product[Prime[j], {j, k}] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

%t 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}]

%Y Cf. A002110, A030017, A051296.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Apr 05 2019