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

1,4

Links

Table of n, a(n) for n=1..22.

Prog

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

Crossrefs

Column 3 of A338805.

Cf. A000005, A059357.

Sequence in context: A085374 A016283 A243880 * A199681 A211403 A008547

Adjacent sequences: A338808 A338809 A338810 * A338812 A338813 A338814

Keyword

nonn

Author

Seiichi Manyama, Nov 10 2020

Status

approved