A117684 Row sums of A117683.

1, 2, 3, 13, 11, 49, 27, 141, 523, 3081, 923, 5509, 1371, 7617, 24391, 84933, 14795, 110329, 20859, 142101, 499843, 1858209, 241211, 2312077, 8417451, 70482153, 251680159, 935093181, 95916299, 1102272481, 131510523, 1270525629, 4572551611, 17189356473

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

a(n) = Sum_{k=1..n} A117683(n,k).

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]);
a[n_]:= a[n]= Sum[T[n, k], {k, n}];
Table[a[n], {n, 40}]

Prog

(Magma)
A034386:= func< n | n eq 0 select 1 else LCM(PrimesInInterval(1, n)) >;
[(&+[Binomial(n, k)*A034386(k)*A034386(n-k)/A034386(n): k in [1..n]]): n in [1..40]]; // G. C. Greubel, Jul 21 2023
(SageMath)
@CachedFunction
def A034386(n): return product(nth_prime(j) for j in range(1, 1+prime_pi(n)))
def A117684(n): return sum(binomial(n, k)*A034386(k)*A034386(n-k)/A034386(n) for k in range(1, n+1))
[A117684(n) for n in range(1, 41)] # G. C. Greubel, Jul 21 2023

Crossrefs

Cf. A117683.

Sequence in context: A046421 A132365 A129671 * A056445 A171483 A100385

Adjacent sequences: A117681 A117682 A117683 * A117685 A117686 A117687

Keyword

nonn

Author

Roger L. Bagula, Apr 12 2006

Extensions

Description simplified, offset corrected by the Assoc. Eds. of the OEIS, Jun 27 2010

Status

approved