A273194 - OEIS

%I #17 Dec 12 2023 18:39:19

%S 1,2,20,1120,30800,1121120,152472320,8277068800,523524601600,

%T 340290991040000,27631628472448000,2491870494969856000,

%U 741331472253532160000,80177849999112785920000,9392262428467497779200000,3554032102932101159649280000,480238587908700169197608960000

%N a(n) = numerator(R(n,3)), where R(n,d) = (Product_{j prime to d} Pochhammer(j/d, n)) / n!.

%C Also the numerators of the nonzero coefficients in the expansion of hypergeom([Seq_{k=1..m-1} k/m], [], (x/m)^m) for m = 3.

%p Hlist := proc(m,size) local H, S;

%p H := m -> hypergeom([seq(k/m, k=1..m-1)], [], (x/m)^m);

%p S := m -> series(H(m), x, (m+1)*size);

%p seq(numer(coeff(S(m), x, m*n)), n=0..size) end:

%p A273194_list := size -> Hlist(3, size);

%p # Alternative:

%p coprimes := n -> select(j -> igcd(j, n) = 1, {$1..n}):

%p R := (n, d) -> mul(pochhammer(j/d, n), j in coprimes(d)) / n!:

%p seq(numer(R(n, 3)), n = 0..16); # _Peter Luschny_, May 20 2021

%Y R(n, 1) = A000012 / A000012.

%Y R(n, 2) = A001790 / A046161.

%Y R(n, 3) = (this sequence) / A344402.

%Y Cf. A273192, A273193.

%K nonn,frac

%O 0,2

%A _Peter Luschny_, Jun 06 2016