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 A363077 #13 Jun 19 2025 05:58:41
%S A363077 0,0,0,0,0,0,1,1,2,3,5,7,12,14,21,27,37,46,63,75,97,119,149,178,222,
%T A363077 260,317,373,447,520,620,713,839,965,1123,1282,1488,1687,1939,2196,
%U A363077 2508,2826,3220,3610,4087,4578,5157,5755,6472,7199,8060,8953,9991,11069,12330,13625,15134,16708,18508
%N A363077 Number of partitions of n such that 5*(least part) + 1 = greatest part.
%F A363077 G.f.: Sum_{k>=1} x^(6*k+1)/Product_{j=k..5*k+1} (1-x^j).
%t A363077 nmax = 100; p = 1; s = 0; Do[p = Simplify[p*(1 - x^(5*k - 4))*(1 - x^(5*k - 3))*(1 - x^(5*k - 2))*(1 - x^(5*k - 1))*(1 - x^(5*k))/(1 - x^k)]; p = Normal[p + O[x]^(nmax + 1)]; s += x^(6*k + 1)/(1 - x^k)/(1 - x^(5*k + 1))/p;, {k, 1, nmax}]; Rest[CoefficientList[Series[s, {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Jun 19 2025 *)
%o A363077 (PARI) my(N=60, x='x+O('x^N)); concat([0, 0, 0, 0, 0, 0], Vec(sum(k=1, N, x^(6*k+1)/prod(j=k, 5*k+1, 1-x^j))))
%Y A363077 Cf. A049820, A237828, A363075, A363076.
%Y A363077 Cf. A237827.
%K A363077 nonn
%O A363077 1,9
%A A363077 _Seiichi Manyama_, May 17 2023