A308228 G.f.: x * Product_{k>=1} 1/(1 - k^k*x^k)^(a(k)/k).

1, 1, 3, 30, 1956, 1224510, 9523018859, 1120383171258352, 2349614928773045360884, 101143220645945325750097689653, 101143220747088551095300901321325558554, 2623394662131051405254078144558922468191548124266

Offset: 1

Author

Ilya Gutkovskiy, May 16 2019

Keywords

• nonn

Crossrefs

Cf. A000081, A023881, A308204, A308231.

Programs

Mathematica

a[n_] := a[n] = SeriesCoefficient[x Product[1/(1 - k^k x^k)^(a[k]/k), {k, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 12}]
a[n_] := a[n] = Sum[Sum[d^k a[d], {d, Divisors[k]}] a[n - k], {k, 1, n - 1}]/(n - 1); a[1] = 1; Table[a[n], {n, 1, 12}]

Formula

Recurrence: a(n+1) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} d^k*a(d) ) * a(n-k+1).