A308231 G.f.: x * Product_{k>=1} (1 + k^k*x^k)^(a(k)/k).

1, 1, 2, 20, 1296, 811314, 6309590183, 742323285862918, 1556765505923600080263, 67013651952683308325826069725, 67013652019696961835287511727174009053, 1738161546565554966558255056834401765693850396861

Offset

1,3

Links

Table of n, a(n) for n=1..12.

Formula

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

Mathematica

a[n_] := a[n] = SeriesCoefficient[x Product[(1 + k^k x^k)^(a[k]/k), {k, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 12}]
a[n_] := a[n] = Sum[Sum[(-1)^(k/d + 1) d^k a[d], {d, Divisors[k]}] a[n - k], {k, 1, n - 1}]/(n - 1); a[1] = 1; Table[a[n], {n, 1, 12}]

Crossrefs

Cf. A004111, A186633, A308205, A308228.

Sequence in context: A239642 A369679 A112359 * A179594 A196749 A263417

Adjacent sequences: A308228 A308229 A308230 * A308232 A308233 A308234

Keyword

nonn

Author

Ilya Gutkovskiy, May 16 2019

Status

approved