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Multiplicative encoding of Losanitsch's triangle (A034851)
1

%I #7 Mar 06 2023 08:52:23

%S 2,6,30,3150,6063750,1717605545906250,2623719141408662719128738281250,

%T 1019408754706474658106933474548666805595768826381331909476074218750

%N Multiplicative encoding of Losanitsch's triangle (A034851)

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LosanitschsTriangle.html">Losanitsch's Triangle</a>.

%F prime(k + 1)^(a(n, k)), where prime(k + 1) is the (k + 1)st prime number (A000040), n is a row number in Losanitsch's triangle and k is a column number (in both the numbering starts from 0) and a(n, k) is the value look-up function for Losanitsch's triangle.

%e The fourth row of Losanitsch's triangle is 1, 2, 4, 2, 1 and the first five primes are 2, 3, 5, 7, 11, therefore the fourth term is 2^1 * 3^2 * 5^4 * 7^2 * 11^1 = 6063750.

%t a[n_, 0] := 1; a[n_, n_] := 1; a[n_, k_] := a[n, k] = a[n - 1, k - 1] + a[n - 1, k] - Binomial[n/2 - 1, (k - 1)/2]Mod[k, 2]Mod[n - 1, 2]; (* The above comes from Weisstein's Mathematica notebook *) multEncLoz[n_] := Times @@ Table[Prime[k + 1]^a[n, k], {k, 0, n}]; Table[multEncLoz[n], {n, 0, 7}]

%Y Cf. A007188 (multiplicative encoding of Pascal's triangle).

%K nonn

%O 0,1

%A _Alonso del Arte_, Dec 17 2008