OFFSET
1,1
COMMENTS
Lah transform of the primes.
LINKS
N. J. A. Sloane, Transforms
FORMULA
E.g.f.: Sum_{k>=1} prime(k)*(x/(1 - x))^k/k!.
MATHEMATICA
Table[Sum[Binomial[n - 1, k - 1] Prime[k] n!/k!, {k, n}], {n, 21}]
nmax = 21; Rest[CoefficientList[Series[Sum[Prime[k] (x/(1 - x))^k/k!, {k, nmax}], {x, 0, nmax}], x] Range[0, nmax]!]
PROG
(PARI) for(n=1, 30, print1(sum(k=1, n, binomial(n-1, k-1)*prime(k)*n!/k!), ", ")) \\ G. C. Greubel, Jul 28 2018
(Magma) [(&+[Binomial(n-1, k-1)*NthPrime(k)*Factorial(n)/Factorial(k): k in [1..n]]): n in [1..30]]; // G. C. Greubel, Jul 28 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 27 2018
STATUS
approved