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Heinz number of row n of Pascal's triangle A007318.
3

%I #7 May 07 2019 17:38:01

%S 2,4,12,100,2548,407044,106023164,136765353124,399090759725236,

%T 4445098474836287524,151287513513627682258436,

%U 12698799587219706700017036196,3463928752077516667634331415766516,2591202267595530693505786197581910681796

%N Heinz number of row n of Pascal's triangle A007318.

%C The Heinz number of a positive integer sequence (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

%C Every odd-indexed term is a square of a squarefree number.

%H <a href="/index/He#Heinz">Index entries for sequences related to Heinz numbers</a>

%F A061395(a(n)) = A001405(n).

%F A056239(a(n)) = A000079(n).

%F A181819(a(n)) = A038754(n + 1).

%e Row n = 5 of Pascal's triangle is (1,5,10,10,5,1), with Heinz number prime(1)*prime(5)*prime(10)*prime(10)*prime(5)*prime(1) = 407044, so a(5) = 407044.

%e The sequence of terms together with their prime indices begins:

%e 2: {1}

%e 4: {1,1}

%e 12: {1,1,2}

%e 100: {1,1,3,3}

%e 2548: {1,1,4,4,6}

%e 407044: {1,1,5,5,10,10}

%e 106023164: {1,1,6,6,15,15,20}

%e 136765353124: {1,1,7,7,21,21,35,35}

%e 399090759725236: {1,1,8,8,28,28,56,56,70}

%e 4445098474836287524: {1,1,9,9,36,36,84,84,126,126}

%t Times@@@Table[Prime[Binomial[n,k]],{n,0,5},{k,0,n}]

%Y Cf. A000040, A001222, A001405, A007318, A056239, A112798, A145519, A215366, A325500, A325503, A325505, A325514.

%K nonn,easy

%O 0,1

%A _Gus Wiseman_, May 06 2019