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

%I A117878 #12 Feb 06 2021 07:44:46
%S A117878 0,1,1,5,5,5,5,5,5,23,29,29,29,119,119,29,29,29,119,119,719,209,209,
%T A117878 209,839,839,5039,5039,209,209,209,839,839,5039,5039,40319,209,209,
%U A117878 209,839,839,5039,5039,40319,362879,209,209,209,839,839,5039,5039,40319,362879
%N A117878 Triangle T(n,k) = A034386(n)*A049614(k) - 1 read by rows.
%H A117878 G. C. Greubel, <a href="/A117878/b117878.txt">Rows n = 1..100 of the triangle, flattened</a>
%F A117878 T(n, k) = A034386(n)*A049614(k) - 1.
%F A117878 T(n, k) = k! * A034386(n)/A034386(k) - 1 = n! * A049614(k)/A049614(n) - 1. - _G. C. Greubel_, Feb 06 2021
%e A117878 The triangle starts in row n=1 as:
%e A117878     0;
%e A117878     1,   1;
%e A117878     5,   5,   5;
%e A117878     5,   5,   5,  23;
%e A117878    29,  29,  29, 119, 119;
%e A117878    29,  29,  29, 119, 119,  719;
%e A117878   209, 209, 209, 839, 839, 5039, 5039;
%e A117878   209, 209, 209, 839, 839, 5039, 5039, 40319;
%e A117878   209, 209, 209, 839, 839, 5039, 5039, 40319, 362879;
%e A117878   209, 209, 209, 839, 839, 5039, 5039, 40319, 362879, 3628799;
%t A117878 A034386[n_]:= Product[Prime[i], {i, PrimePi[n]}];
%t A117878 A049614[n_]:= n!/A034386[n];
%t A117878 Table[A034386[n]*A049614[k] - 1, {n, 10}, {k, n}]//Flatten (* _G. C. Greubel_, Feb 06 2021 *)
%o A117878 (Sage)
%o A117878 def A034386(n): return product( nth_prime(j) for j in (1..prime_pi(n)) )
%o A117878 def A117878(n, k): return factorial(k)*A034386(n)/A034386(k) - 1
%o A117878 flatten([[A117878(n,k) for k in (1..n)] for n in (1..10)]) # _G. C. Greubel_, Feb 06 2021
%Y A117878 Cf. A034386, A049614.
%K A117878 nonn,tabl,less
%O A117878 1,4
%A A117878 _Roger L. Bagula_, May 02 2006
%E A117878 Index in definition and offset corrected by Assoc. Eds. of the OEIS - Jun 15 2010