%I M1726 #24 Oct 12 2024 21:33:20

%S 2,2,6,810,121096582031250,

%T 7114504036033012131698570347034029677643282574273086993343895301222801208496093750

%N Multiplicative encoding of the Eulerian number triangle.

%D R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 254.

%D J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 125.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Alois P. Heinz, <a href="/A007338/b007338.txt">Table of n, a(n) for n = 0..6</a>

%H N. J. A. Sloane, An on-line version of the Encyclopedia of Integer Sequences, <a href="https://doi.org/10.37236/1194">Electronic J. Combinatorics</a>, Vol. 1, no. 1, 1994.

%p a:= n-> mul(ithprime(k+1)^combinat[eulerian1](n, k), k=0..n):

%p seq(a(n), n=0..5); # _Alois P. Heinz_, Jul 26 2017

%t a[0]=2;

%t a[n_]/;n>=1:=Product[Prime[k]^ResourceFunction["EulerianNumber"][n,k],{k,1,n}]

%t Array[a,6,0] (* _Shenghui Yang_, Oct 12 2024 *)

%Y Cf. A173018.

%K nonn

%O 0,1

%A _N. J. A. Sloane_.

%E Last term corrected by _Olivier Gérard_, Mar 15 1997

%E a(0)=2 prepended by _Alois P. Heinz_, Jul 26 2017