OFFSET
1,1
COMMENTS
Stirling transform of primes.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..574
Eric Weisstein's World of Mathematics, Stirling Transform
FORMULA
G.f.: Sum_{k>=1} prime(k)*x^k / Product_{j=1..k} (1 - j*x).
a(n) = Sum_{k=1..n} Stirling2(n,k)*prime(k).
MAPLE
a:= n-> add(ithprime(k)*Stirling2(n, k), k=1..n):
seq(a(n), n=1..30); # Alois P. Heinz, Apr 27 2019
# second Maple program:
b:= proc(n, m) option remember;
`if`(n=0, ithprime(m), m*b(n-1, m)+b(n-1, m+1))
end:
a:= n-> b(n-1, 1):
seq(a(n), n=1..24); # Alois P. Heinz, Aug 03 2021
MATHEMATICA
nmax = 24; Rest[CoefficientList[Series[Sum[Prime[k] (Exp[x] - 1)^k/k!, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!]
nmax = 24; Rest[CoefficientList[Series[Sum[Prime[k] x^k/Product[(1 - j x), {j, 1, k}], {k, 1, nmax}], {x, 0, nmax}], x]]
Table[Sum[StirlingS2[n, k] Prime[k], {k, 1, n}], {n, 1, 24}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 27 2019
STATUS
approved