A308245 G.f.: x * Product_{k>=1} 1/(1 - a(k)*(-x)^k)^((-1)^k).

1, 1, 1, 2, 4, 8, 16, 34, 76, 168, 368, 838, 1964, 4544, 10464, 24658, 58984, 140072, 331456, 795834, 1932228, 4665304, 11227280, 27305882, 66953236, 163418448, 397826496, 976658846, 2412163316, 5935476672, 14576596320, 36023097266, 89458468968

Offset

1,4

Links

Table of n, a(n) for n=1..33.

Formula

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

Mathematica

a[n_] := a[n] = SeriesCoefficient[x Product[1/(1 - a[k] (-x)^k)^((-1)^k), {k, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 33}]
a[n_] := a[n] = Sum[Sum[(-1)^(k + d) d a[d]^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n - 1}]/(n - 1); a[1] = 1; Table[a[n], {n, 1, 33}]

Crossrefs

Cf. A032305, A045648, A049075, A093637, A308246.

Sequence in context: A333647 A045648 A248890 * A209971 A308031 A166354

Adjacent sequences: A308242 A308243 A308244 * A308246 A308247 A308248

Keyword

nonn

Author

Ilya Gutkovskiy, May 16 2019

Status

approved