A308368 G.f. A(x) satisfies: A(x) = x * Product_{k>=1} (1 + A(x^k))/(1 - A(x^k)).
1, 2, 8, 32, 142, 652, 3176, 15916, 82120, 432334, 2315360, 12569180, 69018212, 382630996, 2138788360, 12040391240, 68204335458, 388473940840, 2223439634504, 12781420672112, 73762215951860, 427196466303812, 2482105805258232, 14464061008937328, 84514482402557528
Offset: 1
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 1..200
Programs
-
Mathematica
terms = 25; A[] = 0; Do[A[x] = x Product[(1 + A[x^k])/(1 - A[x^k]), {k, 1, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x] // Rest
Formula
a(n) ~ c * d^n / n^(3/2), where d = 6.218062815147882349... and c = 0.1489003353315039... - Vaclav Kotesovec, Nov 05 2021