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

0,2

Comments

Invert transform of A002110.

Links

Table of n, a(n) for n=0..19.

Formula

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

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}]

Crossrefs

Cf. A002110, A030017, A051296.

Sequence in context: A175937 A175939 A192942 * A141140 A232472 A361829

Adjacent sequences: A307361 A307362 A307363 * A307365 A307366 A307367

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 05 2019

Status

approved