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 A373930 #15 Jun 23 2024 10:31:57
%S A373930 1,5,22,105,518,2555,12565,61748,303470,1491567,7331205,36033501,
%T A373930 177107406,870496256,4278555247,21029425081,103361226864,508028305120,
%U A373930 2496997824041,12272934541014,60322408298439,296489232532277,1457267166329605,7162579146364783
%N A373930 Number of compositions of 7*n-4 into parts 1 and 7.
%H A373930 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (8,-21,35,-35,21,-7,1).
%F A373930 a(n) = A005709(7*n-4).
%F A373930 a(n) = Sum_{k=0..n} binomial(n+2+6*k,n-1-k).
%F A373930 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 A373930 G.f.: x*(1-x)^3/((1-x)^7 - x).
%F A373930 a(n) = n*(1 + n)*(2 + n)*hypergeom([1-n, (3+n)/6, (4+n)/6, (5+n)/6, 1+n/6, (7+n)/6, (8+n)/6], [4/7, 5/7, 6/7, 8/7, 9/7, 10/7], -6^6/7^7)/6. - _Stefano Spezia_, Jun 23 2024
%t A373930 a[n_]:=n*(1 + n)*(2 + n)*HypergeometricPFQ[{1-n, (3+n)/6, (4+n)/6, (5+n)/6, 1+n/6, (7+n)/6, (8+n)/6}, {4/7, 5/7, 6/7, 8/7, 9/7, 10/7}, -6^6/7^7]/6; Array[a,24] (* _Stefano Spezia_, Jun 23 2024 *)
%o A373930 (PARI) a(n) = sum(k=0, n, binomial(n+2+6*k, n-1-k));
%Y A373930 Cf. A099253, A373907, A373928, A373929, A373931, A373932.
%Y A373930 Cf. A005709, A369807.
%K A373930 nonn,easy
%O A373930 1,2
%A A373930 _Seiichi Manyama_, Jun 23 2024