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

3,2

References

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

Links

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

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

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 *)

Prog

(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

Crossrefs

Cf. A008298.

Sequence in context: A260569 A125430 A021764 * A324638 A009470 A111991

Adjacent sequences: A059354 A059355 A059356 * A059358 A059359 A059360

Keyword

nonn

Author

N. J. A. Sloane, Jan 27 2001

Extensions

More terms from Vladeta Jovovic, Dec 28 2001

Status

approved