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A diagonal of triangle in A008298.
4

%I #21 Apr 24 2021 09:55:01

%S 1,18,215,2475,28294,340116,4335596,57773700,831170736,12532005288,

%T 201002619168,3401283910752,60929911689984,1143429812726400,

%U 22572470529457920,468013463441475840,10124124979606179840

%N A diagonal of triangle in A008298.

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

%H Seiichi Manyama, <a href="/A059357/b059357.txt">Table of n, a(n) for n = 3..448</a>

%F 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.

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

%t 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 *)

%o (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

%Y Cf. A008298.

%K nonn

%O 3,2

%A _N. J. A. Sloane_, Jan 27 2001

%E More terms from _Vladeta Jovovic_, Dec 28 2001