A351681 Stirling transform of {1, primes}.

1, 3, 10, 38, 163, 774, 4004, 22315, 132836, 838378, 5574797, 38861142, 282951538, 2146361911, 16931303262, 138694760316, 1178400013929, 10373294706788, 94511288422822, 890334527133081, 8663213736312460, 86975649078035438, 899960154388259079, 9586293761594853220

Offset: 1

Author

Ilya Gutkovskiy, May 07 2022

Keywords

• nonn

Crossrefs

Cf. A008578, A307771, A353406.

Programs

Mathematica

nmax = 24; CoefficientList[Series[Exp[x] - 1 + Sum[Prime[k - 1] (Exp[x] - 1)^k/k!, {k, 2, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[Sum[StirlingS2[n, k] If[k == 1, 1, Prime[k - 1]], {k, 1, n}], {n, 1, 24}]

Formula

E.g.f.: exp(x) - 1 + Sum_{k>=2} prime(k-1) * (exp(x) - 1)^k / k!.

a(n) = Sum_{k=1..n} Stirling2(n,k) * A008578(k).