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

1,1

Links

Table of n, a(n) for 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).

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}]

Crossrefs

Cf. A065091, A307771, A351681.

Sequence in context: A033483 A130522 A006219 * A009268 A024430 A357591

Adjacent sequences: A353403 A353404 A353405 * A353407 A353408 A353409

Keyword

nonn

Author

Ilya Gutkovskiy, May 07 2022

Status

approved