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 A373932 #13 Jun 23 2024 10:32:30
%S A373932 1,3,13,66,330,1624,7973,39173,192539,946375,4651541,22862658,
%T A373932 112371609,552314945,2714670141,13342810843,65580931949,322335276473,
%U A373932 1584302440665,7786967198052,38273537040452,188117350476413,924611109563490,4544534046237850
%N A373932 Number of compositions of 7*n-6 into parts 1 and 7.
%H A373932 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (8,-21,35,-35,21,-7,1).
%F A373932 a(n) = A005709(7*n-6).
%F A373932 a(n) = Sum_{k=0..n} binomial(n+6*k,n-1-k).
%F A373932 a(n) = 8*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).
%F A373932 G.f.: x*(1-x)^5/((1-x)^7 - x).
%F A373932 a(n) = n*hypergeom([1-n,(1+n)/6,(2+n)/6, (3+n)/6, (4+n)/6, (5+n)/6, 1+n/6], [2/7, 3/7, 4/7, 5/7, 6/7, 8/7], -6^6/7^7). - _Stefano Spezia_, Jun 23 2024
%t A373932 a[n_]:=n*HypergeometricPFQ[{1-n,(1+n)/6,(2+n)/6, (3+n)/6, (4+n)/6, (5+n)/6, 1+n/6}, {2/7, 3/7, 4/7, 5/7, 6/7, 8/7}, -6^6/7^7]; Array[a,24] (* _Stefano Spezia_, Jun 23 2024 *)
%o A373932 (PARI) a(n) = sum(k=0, n, binomial(n+6*k, n-1-k));
%Y A373932 Cf. A099253, A373907, A373928, A373929, A373930, A373931.
%Y A373932 Cf. A005709.
%K A373932 nonn,easy
%O A373932 1,2
%A A373932 _Seiichi Manyama_, Jun 23 2024