A336427 - OEIS

%I #18 Jul 22 2020 10:28:26

%S 0,1,5,100,5357,597726,120049592,39381634818,19686000625517,

%T 14233714132535146,14293760060523962630,19298235276251711246358,

%U 34108177389621376109912120,77181320123960021972892515094,219430688163572488543090308547898

%N a(0) = 0; a(n) = 1 + (1/n) * Sum_{k=1..n-1} binomial(n,k)^3 * k * a(k).

%F Sum_{n>=0} a(n) * x^n / (n!)^3 = -log(1 - Sum_{n>=1} x^n / (n!)^3).

%t a[0] = 0; a[n_] := a[n] = 1 + (1/n) Sum[Binomial[n, k]^3 k a[k], {k, 1, n - 1}]; Table[a[n], {n, 0, 14}]

%t nmax = 14; CoefficientList[Series[-Log[1 - Sum[x^k/(k!)^3, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!^3

%Y Cf. A000629, A102223, A193420.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Jul 21 2020