A308206 G.f.: x * Product_{k>=1} 1/(1 - a(k)*x^k)^k.

1, 1, 3, 12, 63, 396, 2926, 24497, 229757, 2377153, 26917186, 330804783, 4387399275, 62455948949, 950123048257, 15384516283921, 264229711285878, 4798448004296966, 91878671010619078, 1850134691327469413, 39088537892778891963, 864610314507158356377

Offset

1,3

Links

Table of n, a(n) for 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).

Mathematica

a[n_] := a[n] = SeriesCoefficient[x Product[1/(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}]

Crossrefs

Cf. A093637, A308204, A308205, A308207.

Sequence in context: A372534 A020123 A307708 * A264151 A186186 A355164

Adjacent sequences: A308203 A308204 A308205 * A308207 A308208 A308209

Keyword

nonn

Author

Ilya Gutkovskiy, May 15 2019

Status

approved