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%I #7 Jul 22 2023 12:11:09
%S 1,2,3,13,11,49,27,141,523,3081,923,5509,1371,7617,24391,84933,14795,
%T 110329,20859,142101,499843,1858209,241211,2312077,8417451,70482153,
%U 251680159,935093181,95916299,1102272481,131510523,1270525629,4572551611,17189356473
%N Row sums of A117683.
%H G. C. Greubel, <a href="/A117684/b117684.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = Sum_{k=1..n} A117683(n,k).
%t f[n_]:= If[PrimeQ[n], 1, n];
%t cf[n_]:= cf[n]= If[n==0, 1, f[n]*cf[n-1]]; (* A049614 *)
%t T[n_, k_]:= T[n, k]= cf[n]/(cf[k]*cf[n-k]);
%t a[n_]:= a[n]= Sum[T[n,k], {k,n}];
%t Table[a[n], {n,40}]
%o (Magma)
%o A034386:= func< n | n eq 0 select 1 else LCM(PrimesInInterval(1, n)) >;
%o [(&+[Binomial(n,k)*A034386(k)*A034386(n-k)/A034386(n): k in [1..n]]): n in [1..40]]; // _G. C. Greubel_, Jul 21 2023
%o (SageMath)
%o @CachedFunction
%o def A034386(n): return product(nth_prime(j) for j in range(1, 1+prime_pi(n)))
%o def A117684(n): return sum(binomial(n,k)*A034386(k)*A034386(n-k)/A034386(n) for k in range(1,n+1))
%o [A117684(n) for n in range(1,41)] # _G. C. Greubel_, Jul 21 2023
%Y Cf. A117683.
%K nonn
%O 1,2
%A _Roger L. Bagula_, Apr 12 2006
%E Description simplified, offset corrected by the Assoc. Eds. of the OEIS, Jun 27 2010
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