This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A181649 #16 Jan 23 2024 12:10:16
%S A181649 1,1,2,3,6,10,18,32,57,101,179,319,566,1006,1786,3174,5638,10016,
%T A181649 17793,31609,56153,99753,177211,314810,559255,993501,1764935,3135366,
%U A181649 5569909,9894819,17577926,31226796,55473705,98547807,175067983,311004383
%N A181649 An INVERT sequence for A010054.
%C A181649 Eigensequence of the sequence array for A010054.
%H A181649 G. C. Greubel, <a href="/A181649/b181649.txt">Table of n, a(n) for n = 0..1000</a>
%F A181649 G.f.: 1/(1-x*Product{k>0,(1 - x^(2k))/(1-x^(2k-1))}).
%F A181649 G.f.: 1 / (1 - x / (1 - x / (1 + x / (1 + x^1 / (1 - x / (1 + x / (1 + x^2 / (1 - x / (1 + x / (1 + x^3 / (1 - x / (1 + x / ...)))))))))))). - _Michael Somos_, Jan 03 2013
%F A181649 a(n) ~ c / r^n, where r = 0.5629116358141452127351993944163442032777187438473224785071475357915... is the root of the equation (-1 + x)*QPochhammer(x^2, x^2) = QPochhammer(1/x, x^2) and c = 0.5730261147067572839709085685318242468812339379480160560847761872213851... - _Vaclav Kotesovec_, Jan 23 2024
%e A181649 1 + x + 2*x^2 + 3*x^3 + 6*x^4 + 10*x^5 + 18*x^6 + 32*x^7 + 57*x^8 + 101*x^9 + ...
%t A181649 eta[q_] := q^(1/24)*QPochhammer[q]; CoefficientList[Series[1/(1 - q^(7/8)*eta[q^2]^2/eta[q]), {q, 0, 50}], q] (* _G. C. Greubel_, Sep 16 2018 *)
%o A181649 (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( 1 / (1 - x * eta(x^2 + A)^2 / eta(x + A)), n))} /* _Michael Somos_, Jan 03 2013 */
%K A181649 easy,nonn
%O A181649 0,3
%A A181649 _Paul Barry_, Nov 03 2010