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 A369794 #30 Jul 05 2024 04:28:23
%S A369794 1,0,0,0,0,1,6,21,56,126,253,474,870,1651,3367,7372,16762,38183,85290,
%T A369794 185573,394555,826752,1724816,3613968,7642004,16313856,35052905,
%U A369794 75487110,162349105,348018300,743376838,1583718457,3370144462,7173308802,15285181447
%N A369794 Expansion of 1/(1 - x^5/(1-x)^6).
%C A369794 Number of compositions of 6*n-5 into parts 5 and 6.
%H A369794 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,7,-1).
%F A369794 a(n) = A107025(n)-A107025(n-1). First differences of A107025.
%F A369794 a(n) = A017837(6*n-5) = Sum_{k=0..floor((6*n-5)/5)} binomial(k,6*n-5-5*k) for n > 0.
%F A369794 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 7*a(n-5) - a(n-6) for n > 6.
%F A369794 a(n) = Sum_{k=0..floor(n/5)} binomial(n-1+k,n-5*k).
%o A369794 (PARI) my(N=40, x='x+O('x^N)); Vec(1/(1-x^5/(1-x)^6))
%Y A369794 Cf. A095263, A290998, A368475.
%Y A369794 Cf. A000389, A099242, A017837, A107025.
%K A369794 nonn,easy
%O A369794 0,7
%A A369794 _Seiichi Manyama_, Feb 01 2024