A308205 G.f.: x * Product_{k>=1} (1 + k*x^k)^a(k).

1, 1, 2, 8, 38, 234, 1679, 13802, 127155, 1297619, 14516296, 176640311, 2322876382, 32831464503, 496399943530, 7995690518504, 136701790293581, 2472679442088700, 47180405307783443, 947116124382018095, 19954735355719570880, 440286840550877179031

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 + 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. A004111, A308204, A308206, A308207.

Sequence in context: A371312 A269509 A307725 * A191016 A293839 A355396

Adjacent sequences: A308202 A308203 A308204 * A308206 A308207 A308208

Keyword

nonn

Author

Ilya Gutkovskiy, May 15 2019

Status

approved