A317421 a(n) = Sum_{k=1..n} binomial(n-1,k-1)*prime(k)*n!/k!.

2, 7, 35, 223, 1711, 15283, 155333, 1766819, 22205615, 305275979, 4553222111, 73179347509, 1260129395189, 23135381385341, 450963438488267, 9298480714769813, 202154606388513675, 4620729025472999443, 110759284511324893795, 2777748141259276697671, 72735279236489471934853

Offset: 1

Author

Ilya Gutkovskiy, Jul 27 2018

Keywords

• nonn

Comments

Lah transform of the primes.

Links

• N. J. A. Sloane, Transforms

Crossrefs

Cf. A000040, A007443.

Programs

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

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]!]

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

Formula

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