login
A325502
Heinz number of row n of Pascal's triangle A007318.
3
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.
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}]
KEYWORD
nonn,easy
AUTHOR
Gus Wiseman, May 06 2019
STATUS
approved