A353406 Stirling transform of odd primes.

3, 8, 25, 91, 376, 1715, 8471, 44838, 252903, 1514213, 9590874, 64056173, 449804453, 3312346950, 25521479277, 205300781275, 1720450321356, 14986361037495, 135393159641569, 1266006310597506, 12228936468908781, 121823473948915769, 1249794986354577736

Offset: 1

Author

Ilya Gutkovskiy, May 07 2022

Keywords

• nonn

Crossrefs

Cf. A065091, A307771, A351681.

Programs

Maple

b:= proc(n, m) option remember;
     `if`(n=0, ithprime(m+1), m*b(n-1, m)+b(n-1, m+1))
    end:
a:= n-> b(n-1, 1):
seq(a(n), n=1..23);  # Alois P. Heinz, May 13 2022

Mathematica

nmax = 23; CoefficientList[Series[Sum[Prime[k + 1] (Exp[x] - 1)^k/k!, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[Sum[StirlingS2[n, k] Prime[k + 1], {k, 1, n}], {n, 1, 23}]

Formula

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

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