A308204 G.f.: x * Product_{k>=1} 1/(1 - k*x^k)^a(k).

1, 1, 3, 12, 64, 402, 2972, 24884, 233224, 2413402, 27321706, 335811420, 4453678055, 63403359154, 964550068984, 15618677100569, 268256266076840, 4871672594496080, 93282009271337370, 1878417037286803586, 39686436905680824542, 877842387051165865980

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^(k/d+1)*a(d) ) * a(n-k+1).

Mathematica

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

Crossrefs

Cf. A000081, A308205, A308206, A308207.

Sequence in context: A371495 A326809 A326557 * A307724 A029851 A201720

Adjacent sequences: A308201 A308202 A308203 * A308205 A308206 A308207

Keyword

nonn

Author

Ilya Gutkovskiy, May 15 2019

Status

approved