|
%I #21 Sep 23 2018 23:02:49
%S 2,3,3,5,9,5,7,45,45,7,11,315,2025,315,11,13,3465,637875,637875,3465,
%T 13,17,45045,2210236875,406884515625,2210236875,45045,17,19,765765,
%U 99560120034375,899311160300888671875,899311160300888671875,99560120034375,765765,19,23,14549535,76239655318123171875,89535527067809533413858673095703125,808760563041730681160065242862701416015625,89535527067809533413858673095703125,76239655318123171875,14549535,23
%N Triangle read by rows: multiplicative version of Pascal's triangle except n-th row begins and ends with (n+1)-st prime.
%F From _Rémy Sigrist_, Sep 02 2018: (Start)
%F A007949(T(n+1, k+1)) = A028326(n, k) for any n >= 0 and k = 0..n.
%F A112765(T(n+1, k+1)) = A007318(n, k) for any n > 0 and k = 0..n.
%F (End)
%e Triangle begins:
%e 2;
%e 3, 3;
%e 5, 9, 5;
%e 7, 45, 45, 7;
%e 11, 315, 2025, 315, 11;
%e 13, 3465, 637875, 637875, 3465, 13;
%e ...
%e Formatted as a symmetric triangle:
%e .
%e 2
%e .
%e 3 3
%e .
%e 5 9 5
%e .
%e 7 45 45 7
%e .
%e 11 315 2025 315 11
%e .
%e 13 3465 637875 637875 3465 13
%e ...
%t t = {{2}};
%t Table[AppendTo[
%t t, {Prime[i],
%t Table[
%t t[[i - 1]][[j]]*t[[i - 1]][[j + 1]], {j,
%t 1, (t[[i - 1]] // Length) - 1}], Prime[i]} // Flatten], {i, 2, 10}] //
%t Last // Flatten
%t t={}; Do[r={}; Do[If[k==0||k==n, m=Prime[n + 1], m=t[[n, k]]t[[n, k + 1]]]; r=AppendTo[r, m], {k, 0, n}]; AppendTo[t, r], {n, 0, 10}]; t (* _Vincenzo Librandi_, Sep 03 2018 *)
%Y Cf. A000040, A007318, A007949, A028326, A051599, A080046, A112765.
%K nonn,tabl
%O 0,1
%A _Philipp O. Tsvetkov_, Aug 02 2018
|
