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 A373928 #19 Jul 28 2024 13:49:41
%S A373928 1,7,35,168,819,4025,19796,97315,478304,2350860,11554621,56791883,
%T A373928 279136551,1371977475,6743373646,33144194898,162906243014,
%U A373928 800696596250,3935484773527,19343207491818,95073338508548,467292702057555,2296779231936167,11288844908179562
%N A373928 Number of compositions of 7*n-2 into parts 1 and 7.
%H A373928 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (8,-21,35,-35,21,-7,1).
%F A373928 a(n) = A005709(7*n-2).
%F A373928 a(n) = Sum_{k=0..n} binomial(n+4+6*k,n-1-k).
%F A373928 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 A373928 G.f.: x*(1-x)/((1-x)^7 - x).
%F A373928 a(n) = n*(1 + n)*(2 + n)*(3 + n)*(4 + n)*hypergeom([1-n, (5+n)/6, 1+n/6, (7+n)/6, (8+n)/6, (9+n)/6, (10+n)/6], [6/7, 8/7, 9/7, 10/7, 11/7, 12/7], -6^6/7^7)/120. - _Stefano Spezia_, Jun 23 2024
%t A373928 a[n_]:= n*(1 + n)*(2 + n)*(3 + n)*(4 + n)*HypergeometricPFQ[{1-n, (5+n)/6, 1+n/6, (7+n)/6, (8+n)/6, (9+n)/6, (10+n)/6}, {6/7, 8/7, 9/7, 10/7, 11/7, 12/7}, -6^6/7^7]/120; Array[a,24] (* _Stefano Spezia_, Jun 23 2024 *)
%t A373928 LinearRecurrence[{8,-21,35,-35,21,-7,1},{1,7,35,168,819,4025,19796},40] (* _Harvey P. Dale_, Jul 28 2024 *)
%o A373928 (PARI) a(n) = sum(k=0, n, binomial(n+4+6*k, n-1-k));
%Y A373928 Cf. A099253, A373907, A373929, A373930, A373931, A373932.
%Y A373928 Cf. A005709, A369805, A369837.
%K A373928 nonn,easy
%O A373928 1,2
%A A373928 _Seiichi Manyama_, Jun 23 2024