OFFSET
1,7
LINKS
G. C. Greubel, Rows n = 1..50 of the triangle, flattened
FORMULA
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 1, 1;
4, 4, 4, 1;
1, 4, 4, 1, 1;
6, 6, 24, 6, 6, 1;
1, 6, 6, 6, 6, 1, 1;
8, 8, 48, 12, 48, 8, 8, 1;
9, 72, 72, 108, 108, 72, 72, 9, 1;
MATHEMATICA
f[n_]:= If[PrimeQ[n], 1, n];
cf[n_]:= cf[n]= If[n==0, 1, f[n]*cf[n-1]]; (* A049614 *)
T[n_, k_]:= T[n, k]= cf[n]/(cf[k]*cf[n-k]);
Table[T[n, k], {n, 12}, {k, n}]//Flatten
PROG
(PARI) primorial(n)=prod(i=1, primepi(n), prime(i))
T(n, m)=binomial(n, m)*primorial(m)*primorial(n-m)/primorial(n) \\ Charles R Greathouse IV, Jan 16 2012
(Magma)
A049614:= func< n | n le 1 select 1 else Factorial(n)/(&*[NthPrime(j): j in [1..#PrimesUpTo(n)]]) >;
[A117683(n, k): k in [1..n], n in [1..12]]; // G. C. Greubel, Jul 21 2023
(SageMath)
def A049614(n): return factorial(n)/product(nth_prime(j) for j in range(1, 1+prime_pi(n)))
flatten([[A117683(n, k) for k in range(1, n+1)] for n in range(1, 13)]) # G. C. Greubel, Jul 21 2023
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Apr 12 2006
EXTENSIONS
Edited by the Associate Editors of the OEIS, Aug 18 2009
Edited by G. C. Greubel, Jul 21 2023
STATUS
approved