A338811 a(n) = (n!/6) * Sum_{i,j,k > 0 and i+j+k=n} d(i)*d(j)*d(k)/(i*j*k), where d(n) is the number of divisors of n.

0, 0, 1, 12, 100, 870, 7588, 73808, 764524, 8448120, 103816944, 1334764728, 18483356736, 274780501632, 4371694872192, 71815113008640, 1282261138007040, 23828058693642240, 468231649812725760, 9599857257164820480, 205863214718290636800, 4646428416182168985600

Offset: 1

Author

Seiichi Manyama, Nov 10 2020

Keywords

• nonn

Crossrefs

Column 3 of A338805.

Cf. A000005, A059357.

Programs

PARI

{a(n) = my(u='u); n!*polcoef(polcoef(prod(k=1, n, (1-x^k+x*O(x^n))^(-u/k)), n), 3)}