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 A360090 #19 Jul 13 2025 23:27:32
%S A360090 1,1,6,21,71,251,882,3088,10829,37975,133146,466852,1636944,5739647,
%T A360090 20125051,70564951,247423522,867546829,3041899638,10665883415,
%U A360090 37398034921,131129599227,459782762029,1612146986543,5652708454881,19820223058176,69496108849357
%N A360090 a(n) = Sum_{k=0..n} binomial(5*k,n-k).
%C A360090 The number of ways to place non-overlapping Young diagrams of shape (2,1,1,1,1) on an 9 by n rectangle. - _Per Alexandersson_, Jul 01 2025
%H A360090 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,5,10,10,5,1).
%F A360090 a(n) = a(n-1) + 5*a(n-2) + 10*a(n-3) + 10*a(n-4) + 5*a(n-5) + a(n-6).
%F A360090 G.f.: 1/(1 - x*(1+x)^5).
%p A360090 seq(add(binomial(5*k,n-k),k=0..n), n=0..50); # _Robert Israel_, Jul 09 2025
%o A360090 (PARI) a(n) = sum(k=0, n, binomial(5*k, n-k));
%o A360090 (PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-x*(1+x)^5))
%Y A360090 Cf. A002478, A099234, A099235.
%K A360090 nonn,easy
%O A360090 0,3
%A A360090 _Seiichi Manyama_, Jan 25 2023