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A117878
Triangle T(n,k) = A034386(n)*A049614(k) - 1 read by rows.
1
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
1,4
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
EXAMPLE
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;
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 *)
PROG
(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
CROSSREFS
Sequence in context: A372613 A355588 A289119 * A291497 A241154 A094636
KEYWORD
nonn,tabl,less
AUTHOR
Roger L. Bagula, May 02 2006
EXTENSIONS
Index in definition and offset corrected by Assoc. Eds. of the OEIS - Jun 15 2010
STATUS
approved