A347948 E.g.f.: 1 / (1 - Sum_{k>=1} x^prime(k) / prime(k)!).
1, 0, 1, 1, 6, 21, 110, 673, 4312, 34260, 280212, 2648581, 26580840, 292468333, 3453838544, 43672689816, 590203920256, 8458029201433, 128528293405392, 2059731511022935, 34762308371221224, 615898019175914166, 11432263502365894916, 221855824404176472115
Offset: 0
Keywords
Programs
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Mathematica
nmax = 23; CoefficientList[Series[1/(1 - Sum[x^Prime[k]/Prime[k]!, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]! a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] Boole[PrimeQ[k]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 23}]
Formula
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * A010051(k) * a(n-k).