A374852 a(n) = (1/3)*A054640(n) for n >= 1.

1, 4, 24, 192, 2304, 32256, 580608, 11612160, 278691840, 8360755200, 267544166400, 10166678323200, 427000489574400, 18788021541273600, 901825033981132800, 48698551834981171200, 2921913110098870272000, 181158612826129956864000, 12318785672176837066752000

Offset: 1

Author

Clark Kimberling, Aug 05 2024

Keywords

• nonn

Comments

a(n+1)/a(n) is an integer for n>=0, so (a(n)) is a divisibility sequence.

Crossrefs

Cf. A000040, A374848.

Programs

Mathematica

s[n_] := 1; t[n_] := Prime[n];
u[n_] := Product[s[k] + t[n + 1 - k], {k, 1, n}]
(1/3) Table[u[n], {n, 1, 25}]

Formula

a(n) = (1/3)(s**t)(n) for n>=1, where s = (1,1,1,...), t = A000040 (the primes), and ** denotes obverse convolution, as in A374848.

a(n) = 2n*a(n-1) for n >= 2.