A059357 A diagonal of triangle in A008298.

1, 18, 215, 2475, 28294, 340116, 4335596, 57773700, 831170736, 12532005288, 201002619168, 3401283910752, 60929911689984, 1143429812726400, 22572470529457920, 468013463441475840, 10124124979606179840

Offset: 3

Author

N. J. A. Sloane, Jan 27 2001

Keywords

• nonn

References

• L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 159.

Links

• Seiichi Manyama, Table of n, a(n) for n = 3..448

Crossrefs

Cf. A008298.

Programs

Mathematica

nmax = 20; Table[n!/6 * Sum[Sum[Sum[If[i + j + k == n, DivisorSigma[1,i] * DivisorSigma[1,j] * DivisorSigma[1,k] / (i*j*k), 0], {k, 1, n}], {j, 1, n}], {i, 1, n}], {n, 3, nmax}] (* Vaclav Kotesovec, Nov 09 2020 *)

PARI

{a(n) = my(t='t); n!*polcoef(polcoef(prod(k=1, n, (1-x^k+x*O(x^n))^(-t)), n), 3)} \\ Seiichi Manyama, Nov 07 2020

Formula

a(n) = (n!/6) * Sum_{i,j,k > 0 and i+j+k=n} sigma(i)*sigma(j)*sigma(k)/(i*j*k). - Seiichi Manyama, Nov 09 2020.

E.g.f.: -(1/6) * log( Product_{k>=1} (1 - x^k) )^3. - Ilya Gutkovskiy, Apr 24 2021

Extensions

More terms from Vladeta Jovovic, Dec 28 2001