A338788 - OEIS

%I #16 Nov 10 2020 02:19:13

%S 0,0,1,6,95,585,8974,70252,1178540,10683180,201213936,2151034776,

%T 46320457248,557515105056,12980593545984,179077693449600,

%U 4696518067511040,71418673681171200,2026061283912560640,33687422807179092480,1055027603388725452800,19337685190135751577600

%N a(n) = (n!/6) * Sum_{i,j,k > 0 and i+j+k=n} A000593(i)*A000593(j)*A000593(k)/(i*j*k).

%H Seiichi Manyama, <a href="/A338788/b338788.txt">Table of n, a(n) for n = 1..448</a>

%t nmax = 50; A000593 = Table[Sum[Mod[d, 2] d, {d, Divisors[n]}], {n, 1, nmax}]; Table[n!/6 * Sum[Sum[Sum[If[i + j + k == n, A000593[[i]] * A000593[[j]] * A000593[[k]] / (i*j*k), 0], {k, 1, n}], {j, 1, n}], {i, 1, n}], {n, 1, 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)}

%Y Column 3 of A075525.

%Y Cf. A000593, A059357.

%K nonn

%O 1,4

%A _Seiichi Manyama_, Nov 09 2020