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 A330643 #19 Dec 28 2024 09:51:18
%S A330643 1,1,2,3,5,7,11,15,22,30,42,56,77,101,135,176,231,297,385,490,627,792,
%T A330643 1002,1255,1575,1958,2436,3010,3718,4565,5604,6842,8349,10143,12310,
%U A330643 14883,17976,21635,26010,31175,37318,44547,53109,63153,74996,88850,105113,124078,146256,172032,202056,236844
%N A330643 a(n) is the number of partitions of n with Durfee square of size <= 5.
%H A330643 Andrew Howroyd, <a href="/A330643/b330643.txt">Table of n, a(n) for n = 0..1000</a>
%H A330643 <a href="/index/Rec#order_30">Index entries for linear recurrences with constant coefficients</a>, signature (2, 1, -2, -1, -2, 0, 2, 6, 2, -3, -6, -5, -2, 3, 12, 3, -2, -5, -6, -3, 2, 6, 2, 0, -2, -1, -2, 1, 2, -1).
%F A330643 a(n) = A000041(n), 0 <= n <= 35.
%F A330643 a(n) = A330642(n), 0 <= n <= 24.
%F A330643 a(n) = A330642(n) + A117487(n-24), n >= 25.
%F A330643 a(n) = n + A006918(n-3) + A117485(n) + A117486(n-16) + A117487(n-24), n >= 25.
%F A330643 G.f.: Sum_{k=0..5} x^(k^2)/(Product_{j=1..k} (1 - x^j))^2. - _Andrew Howroyd_, Dec 27 2024
%o A330643 (PARI) seq(n) = Vec(sum(k=0, 5, x^(k^2)/prod(j=1, k, 1 - x^j)^2) + O(x*x^n)) \\ _Andrew Howroyd_, Dec 27 2024
%Y A330643 Cf. A000041, A006918, A008805, A028310, A115994, A115720, A117485, A117486, A117487, A330640, A330641, A330642.
%K A330643 nonn
%O A330643 0,3
%A A330643 _Omar E. Pol_, Dec 24 2019