A153046 Multiplicative encoding of Losanitsch's triangle (A034851).

2, 6, 30, 3150, 6063750, 1717605545906250, 2623719141408662719128738281250, 1019408754706474658106933474548666805595768826381331909476074218750

Offset: 0

Author

Alonso del Arte, Dec 17 2008

Keywords

• nonn

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, Losanitsch's Triangle.

Crossrefs

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

Programs

Mathematica

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}]

Formula

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.