A117878 Triangle T(n,k) = A034386(n)*A049614(k) - 1 read by rows.

0, 1, 1, 5, 5, 5, 5, 5, 5, 23, 29, 29, 29, 119, 119, 29, 29, 29, 119, 119, 719, 209, 209, 209, 839, 839, 5039, 5039, 209, 209, 209, 839, 839, 5039, 5039, 40319, 209, 209, 209, 839, 839, 5039, 5039, 40319, 362879, 209, 209, 209, 839, 839, 5039, 5039, 40319, 362879

Offset: 1

Author

Roger L. Bagula, May 02 2006

Keywords

• nonn
• tabl
• less

Examples

			The triangle starts in row n=1 as:
    0;
    1,   1;
    5,   5,   5;
    5,   5,   5,  23;
   29,  29,  29, 119, 119;
   29,  29,  29, 119, 119,  719;
  209, 209, 209, 839, 839, 5039, 5039;
  209, 209, 209, 839, 839, 5039, 5039, 40319;
  209, 209, 209, 839, 839, 5039, 5039, 40319, 362879;
  209, 209, 209, 839, 839, 5039, 5039, 40319, 362879, 3628799;
		

Links

• G. C. Greubel, Rows n = 1..100 of the triangle, flattened

Crossrefs

Cf. A034386, A049614.

Programs

Mathematica

A034386[n_]:= Product[Prime[i], {i, PrimePi[n]}];
A049614[n_]:= n!/A034386[n];
Table[A034386[n]*A049614[k] - 1, {n, 10}, {k, n}]//Flatten (* G. C. Greubel, Feb 06 2021 *)

Sage

def A034386(n): return product( nth_prime(j) for j in (1..prime_pi(n)) )
def A117878(n, k): return factorial(k)*A034386(n)/A034386(k) - 1
flatten([[A117878(n,k) for k in (1..n)] for n in (1..10)]) # G. C. Greubel, Feb 06 2021

Formula

T(n, k) = A034386(n)*A049614(k) - 1.

T(n, k) = k! * A034386(n)/A034386(k) - 1 = n! * A049614(k)/A049614(n) - 1. - G. C. Greubel, Feb 06 2021

Extensions

Index in definition and offset corrected by Assoc. Eds. of the OEIS - Jun 15 2010