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 A293423 #16 Jul 18 2025 20:30:57
%S A293423 1,3,9,17,36,63,118,195,333,528,852,1305,2020,3012,4518,6583,9624,
%T A293423 13761,19698,27702,38952,54000,74784,102357,139882,189297,255690,
%U A293423 342497,457824,607617,804656,1058970,1390545,1815984,2366268,3068388,3970008,5114382,6574266
%N A293423 Expansion of Product_{k>0} (1 - q^(3*k))^5/((1 - q^k)^3*(1 - q^(6*k))^2).
%H A293423 Seiichi Manyama, <a href="/A293423/b293423.txt">Table of n, a(n) for n = 0..10000</a>
%F A293423 a(n) ~ 5^(1/4) * exp(sqrt(10*n)*Pi/3) / (9*2^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Oct 09 2017
%p A293423 b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i>1, b(n, i-1), 0)+
%p A293423 add((p-> p+[0, p[1]])(b(n-i*j, min(n-i*j, i-1))*j), j=`if`(i=1, n, 1..n/i)))
%p A293423 end:
%p A293423 a:= n-> (p-> 2*p[2]+p[1])(b(n$2)):
%p A293423 seq(a(n), n=0..38); # _Alois P. Heinz_, Jul 18 2025
%t A293423 nmax = 50; CoefficientList[Series[Product[(1 - x^(3*k))^5 / ((1 - x^k)^3 * (1 - x^(6*k))^2), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Oct 09 2017 *)
%Y A293423 Cf. A293421.
%K A293423 nonn
%O A293423 0,2
%A A293423 _Seiichi Manyama_, Oct 08 2017