A308207 G.f.: x * Product_{k>=1} (1 + a(k)*x^k)^k.

1, 1, 2, 8, 39, 240, 1723, 14165, 130459, 1331530, 14894260, 181259007, 2383643794, 33692516860, 509433237073, 8205927166103, 140299345385359, 2537807239717465, 48423816128109123, 972089365983087479, 20481094574718083726, 451904232651000126082

Offset: 1

Author

Ilya Gutkovskiy, May 15 2019

Keywords

• nonn

Crossrefs

Cf. A032305, A308204, A308205, A308206.

Programs

Mathematica

a[n_] := a[n] = SeriesCoefficient[x Product[(1 + a[k] x^k)^k, {k, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 22}]
a[n_] := a[n] = -Sum[Sum[d^2 (-a[d])^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n - 1}]/(n - 1); a[1] = 1; Table[a[n], {n, 1, 22}]

Formula

Recurrence: a(n+1) = -(1/n) * Sum_{k=1..n} ( Sum_{d|k} d^2*(-a(d))^(k/d) ) * a(n-k+1).