A298260
G.f. A(x) satisfies A(x) = Product_{k>=1} 1/(1 + x^k*A(x)).
Original entry on oeis.org
1, -1, 1, -3, 8, -22, 62, -182, 550, -1694, 5294, -16758, 53635, -173260, 564129, -1849448, 6099972, -20227036, 67390803, -225485432, 757361764, -2552692848, 8631144354, -29268108530, 99511629658, -339167845294, 1158607479710, -3966129297519, 13603228472518
Offset: 0
G.f. A(x) = 1 - x + x^2 - 3*x^3 + 8*x^4 - 22*x^5 + 62*x^6 - 182*x^7 + 550*x^8 - 1694*x^9 + ...
G.f. A(x) satisfies A(x) = 1/((1 + x*A(x)) * (1 + x^2*A(x)) * (1 + x^3*A(x)) * ... ).
A302171
G.f. A(x) satisfies: A(x) = Product_{k>=1} 1/(1 - x^k*A(x))^k.
Original entry on oeis.org
1, 1, 4, 14, 54, 213, 880, 3724, 16143, 71227, 319067, 1447160, 6633530, 30682425, 143028870, 671293632, 3169572659, 15044993968, 71752624923, 343658572717, 1652266087698, 7971518032791, 38581202763318, 187269381724629, 911404238805468, 4446493502832481, 21742327471261176
Offset: 0
G.f. A(x) = 1 + x + 4*x^2 + 14*x^3 + 54*x^4 + 213*x^5 + 880*x^6 + 3724*x^7 + 16143*x^8 + ...
G.f. A(x) satisfies: A(x) = 1/((1 - x*A(x)) * (1 - x^2*A(x))^2 * (1 - x^3*A(x))^3 * ...).
-
nmax = 30; A[] = 0; Do[A[x] = 1/Product[(1 - x^k*A[x])^k, {k, 1, nmax}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] (* Vaclav Kotesovec, Sep 26 2023 *)
A302288
G.f. A(x) satisfies: A(x) = Product_{k>=1} 1/(1 - k*x^k*A(x)).
Original entry on oeis.org
1, 1, 4, 14, 55, 217, 908, 3864, 16894, 75078, 338862, 1548055, 7147427, 33294790, 156305144, 738753341, 3512431392, 16788169689, 80619590577, 388785776751, 1882063496033, 9142361671588, 44550166132194, 217716111661799, 1066792279046783, 5239947708977474, 25795965431819883
Offset: 0
G.f. A(x) = 1 + x + 4*x^2 + 14*x^3 + 55*x^4 + 217*x^5 + 908*x^6 + 3864*x^7 + 16894*x^8 + 75078*x^9 + 338862*x^10 + ...
G.f. A(x) satisfies: A(x) = 1/((1 - x*A(x)) * (1 - 2*x^2*A(x)) * (1 - 3*x^3*A(x)) * (1 - 4*x^4*A(x)) * ...).
Showing 1-3 of 3 results.