login
A352060
a(n) = (n - 1)! * omega(n), where omega(n) = number of distinct primes dividing n (A001221).
2
0, 1, 2, 6, 24, 240, 720, 5040, 40320, 725760, 3628800, 79833600, 479001600, 12454041600, 174356582400, 1307674368000, 20922789888000, 711374856192000, 6402373705728000, 243290200817664000, 4865804016353280000, 102181884343418880000, 1124000727777607680000
OFFSET
1,3
FORMULA
E.g.f.: -Sum_{p prime} log(1-x^p)/p.
MATHEMATICA
a[n_] := (n-1)! * PrimeNu[n]; Array[a, 25] (* Amiram Eldar, Mar 02 2022 *)
PROG
(PARI) a(n) = (n-1)!*omega(n);
(PARI) my(N=40, x='x+O('x^N)); concat(0, Vec(serlaplace(-sum(k=1, N, isprime(k)*log(1-x^k)/k))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 02 2022
STATUS
approved