This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A317421 #9 Sep 08 2022 08:46:22
%S A317421 2,7,35,223,1711,15283,155333,1766819,22205615,305275979,4553222111,
%T A317421 73179347509,1260129395189,23135381385341,450963438488267,
%U A317421 9298480714769813,202154606388513675,4620729025472999443,110759284511324893795,2777748141259276697671,72735279236489471934853
%N A317421 a(n) = Sum_{k=1..n} binomial(n-1,k-1)*prime(k)*n!/k!.
%C A317421 Lah transform of the primes.
%H A317421 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A317421 E.g.f.: Sum_{k>=1} prime(k)*(x/(1 - x))^k/k!.
%t A317421 Table[Sum[Binomial[n - 1, k - 1] Prime[k] n!/k!, {k, n}], {n, 21}]
%t A317421 nmax = 21; Rest[CoefficientList[Series[Sum[Prime[k] (x/(1 - x))^k/k!, {k, nmax}], {x, 0, nmax}], x] Range[0, nmax]!]
%o A317421 (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
%o A317421 (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
%Y A317421 Cf. A000040, A007443.
%K A317421 nonn
%O A317421 1,1
%A A317421 _Ilya Gutkovskiy_, Jul 27 2018