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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 11 2019
STATUS
approved