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A153046 Multiplicative encoding of Losanitsch's triangle (A034851) 1
2, 6, 30, 3150, 6063750, 1717605545906250, 2623719141408662719128738281250, 1019408754706474658106933474548666805595768826381331909476074218750 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..7.

Weisstein, Eric W. "Losanitsch's Triangle." http://mathworld.wolfram.com/LosanitschsTriangle.html

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.

EXAMPLE

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.

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}]

CROSSREFS

Cf. A007188, multiplicative encoding of Pascal's triangle.

Sequence in context: A102927 A227105 A127295 * A088260 A232171 A231816

Adjacent sequences:  A153043 A153044 A153045 * A153047 A153048 A153049

KEYWORD

nonn

AUTHOR

Alonso del Arte, Dec 17 2008

STATUS

approved

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Last modified November 20 14:54 EST 2019. Contains 329337 sequences. (Running on oeis4.)