A325502 Heinz number of row n of Pascal's triangle A007318.

2, 4, 12, 100, 2548, 407044, 106023164, 136765353124, 399090759725236, 4445098474836287524, 151287513513627682258436, 12698799587219706700017036196, 3463928752077516667634331415766516, 2591202267595530693505786197581910681796

Offset

0,1

Comments

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

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

Links

Table of n, a(n) for n=0..13.

Index entries for sequences related to Heinz numbers

Formula

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

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

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

Example

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.
The sequence of terms together with their prime indices begins:
                    2: {1}
                    4: {1,1}
                   12: {1,1,2}
                  100: {1,1,3,3}
                 2548: {1,1,4,4,6}
               407044: {1,1,5,5,10,10}
            106023164: {1,1,6,6,15,15,20}
         136765353124: {1,1,7,7,21,21,35,35}
      399090759725236: {1,1,8,8,28,28,56,56,70}
  4445098474836287524: {1,1,9,9,36,36,84,84,126,126}

Mathematica

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

Crossrefs

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

Sequence in context: A326945 A309718 A230814 * A038791 A327563 A326950

Adjacent sequences: A325499 A325500 A325501 * A325503 A325504 A325505

Keyword

nonn,easy

Author

Gus Wiseman, May 06 2019

Status

approved