A308246 G.f.: x * Product_{k>=1} (1 + a(k)*(-x)^k)^((-1)^k).

1, 1, 2, 4, 8, 18, 44, 104, 246, 620, 1600, 4082, 10436, 27360, 73046, 193296, 509984, 1371214, 3727792, 10065872, 27145058, 74142688, 204005440, 558475342, 1527058912, 4213709856, 11694035010, 32331790700, 89266126856, 248240818282, 693599213260

Offset

1,3

Links

Table of n, a(n) for n=1..31.

Formula

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

Mathematica

a[n_] := a[n] = SeriesCoefficient[x Product[(1 + a[k] (-x)^k)^((-1)^k), {k, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 31}]
a[n_] := a[n] = Sum[Sum[(-1)^(k/d + k + d + 1) 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, 31}]

Crossrefs

Cf. A032305, A045648, A049075, A093637, A308245.

Sequence in context: A059221 A193617 A233139 * A114203 A339837 A100132

Adjacent sequences: A308243 A308244 A308245 * A308247 A308248 A308249

Keyword

nonn

Author

Ilya Gutkovskiy, May 16 2019

Status

approved