A308060 G.f. A(x) satisfies: A(x) = x * exp(Sum_{i>=1} Sum_{j>=1} (-1)^(j+1)*A(x^(i*j))/j).

1, 1, 2, 5, 11, 26, 65, 161, 412, 1074, 2841, 7599, 20582, 56202, 154760, 429052, 1196802, 3356107, 9456737, 26760173, 76017365, 216693521, 619663800, 1777141141, 5110235884, 14730604451, 42557910762, 123210505445, 357403386959, 1038616488923, 3023329186466, 8814593734152

Offset

1,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..500

Formula

G.f.: x * Product_{i>=1, j>=1} (1 + x^(i*j))^a(j).

a(n) ~ c * d^n / n^(3/2), where d = 3.05850813076802274498884492525... and c = 0.46090575889706771724968759... - Vaclav Kotesovec, Nov 05 2021

Mathematica

terms = 32; A[_] = 0; Do[A[x_] = x Exp[Sum[Sum[(-1)^(j + 1) A[x^(i j)]/j, {j, 1, terms}], {i, 1, terms}]] + O[x]^(terms + 1) // Normal, terms + 1]; Rest[CoefficientList[A[x], x]]
a[n_] := a[n] = SeriesCoefficient[x Product[Product[(1 + x^(i j))^a[j], {j, 1, n - 1}], {i, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 32}]

Crossrefs

Cf. A004111, A179467.

Sequence in context: A308154 A182053 A306563 * A235496 A025245 A300125

Adjacent sequences: A308057 A308058 A308059 * A308061 A308062 A308063

Keyword

nonn

Author

Ilya Gutkovskiy, May 11 2019

Status

approved