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

1,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..200

Formula

a(n) ~ c * d^n / n^(3/2), where d = 6.218062815147882349... and c = 0.1489003353315039... - Vaclav Kotesovec, Nov 05 2021

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

Crossrefs

Cf. A050383, A091865.

Sequence in context: A150858 A150859 A150860 * A072243 A150861 A150862

Adjacent sequences: A308365 A308366 A308367 * A308369 A308370 A308371

Keyword

nonn

Author

Ilya Gutkovskiy, May 22 2019

Status

approved