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 A363076 #12 Jun 19 2025 05:57:41
%S A363076 0,0,0,0,0,1,1,2,3,5,8,10,14,19,25,33,41,51,65,79,97,116,140,165,198,
%T A363076 233,272,316,369,422,493,561,643,731,835,943,1072,1205,1359,1524,1717,
%U A363076 1911,2147,2387,2665,2960,3295,3640,4049,4469,4950,5455,6028,6622,7310,8024,8826,9676,10632,11627,12765
%N A363076 Number of partitions of n such that 4*(least part) + 1 = greatest part.
%F A363076 G.f.: Sum_{k>=1} x^(5*k+1)/Product_{j=k..4*k+1} (1-x^j).
%t A363076 nmax = 100; p = 1; s = 0; Do[p = Simplify[p*(1 - x^(4*k - 3))*(1 - x^(4*k - 2))*(1 - x^(4*k - 1))*(1 - x^(4*k))/(1 - x^k)]; p = Normal[p + O[x]^(nmax + 1)]; s += x^(5*k + 1)/(1 - x^k)/(1 - x^(4*k + 1))/p;, {k, 1, nmax}]; Rest[CoefficientList[Series[s, {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Jun 19 2025 *)
%o A363076 (PARI) my(N=70, x='x+O('x^N)); concat([0, 0, 0, 0, 0], Vec(sum(k=1, N, x^(5*k+1)/prod(j=k, 4*k+1, 1-x^j))))
%Y A363076 Cf. A049820, A237828, A363075, A363077.
%Y A363076 Cf. A237826.
%K A363076 nonn
%O A363076 1,8
%A A363076 _Seiichi Manyama_, May 17 2023