cp's OEIS Frontend

A130767 a(n) = product{k=1 to n} (k-th integer from among those positive integers which are coprime to (n+1-k)).

%I A130767 #13 Mar 14 2018 04:25:35
%S A130767 1,2,9,40,420,2700,56595,419328,8820900,88488400,2327925600,
%T A130767 38767286880,1912404574080,21612951360000,644047087612500,
%U A130767 10985391056640000,634391869996684800,14046187624838328960,764077915447610400000,15840110879873280000000,755098009918296312668400
%N A130767 a(n) = product{k=1 to n} (k-th integer from among those positive integers which are coprime to (n+1-k)).
%C A130767 a(n) is the product of the terms in the n-th antidiagonal of the A126572 array. - _Michel Marcus_, Mar 14 2018
%e A130767 The integers coprime to 1 are: 1,2,3,4,5,6,... The 5th of these is 5. The integers coprime to 2 are: 1,3,5,7,9,... The 4th of these is 7. The integers coprime to 3 are: 1,2,4,5,7,... The 3rd of these is 4. The integers coprime to 4 are: 1,3,5,... The 2nd of these is 3. And the integers coprime to 5 are: 1,2,3,4,6,... The first of these is 1. So a(5) = 5 * 7 * 4 * 3 * 1 = 420.
%o A130767 (PARI) cop(k, j) = {my(nbc = 0, i = 0); while (nbc != j, i++; if (gcd(i,k)==1, nbc++)); i;}
%o A130767 a(n) = {my(vc = vector(n, k, cop(k, n-k+1))); prod(k=1, n, vc[k]);} \\ _Michel Marcus_, Mar 14 2018
%Y A130767 Cf. A126572, A132273, A132421.
%K A130767 nonn
%O A130767 1,2
%A A130767 _Leroy Quet_, Aug 18 2007
%E A130767 More terms from _Michel Marcus_, Mar 14 2018