A308433 G.f.: x * (d/dx) x * Product_{k>=1} (1 + x^k)^(a(k)/k).

1, 2, 3, 8, 15, 36, 84, 200, 468, 1130, 2717, 6576, 15938, 38780, 94485, 230816, 564553, 1383318, 3393742, 8336960, 20502216, 50472928, 124369832, 306729456, 757078000, 1870040822, 4622317812, 11432698704, 28294211920, 70063292310, 173584768088, 430276174016, 1067049650238

Offset

1,2

Links

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

Formula

L.g.f.: x * exp(Sum_{k>=1} ( Sum_{d|k} (-1)^(k/d+1)*a(d) ) * x^k/k).

a(n) = n * A004111(n).

Mathematica

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

Crossrefs

Cf. A004111, A055544.

Sequence in context: A080206 A132862 A055543 * A049957 A151255 A147999

Adjacent sequences: A308430 A308431 A308432 * A308434 A308435 A308436

Keyword

nonn

Author

Ilya Gutkovskiy, May 26 2019

Status

approved