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 A073376 #14 Sep 30 2022 02:00:16
%S A073376 1,7,42,196,826,3150,11256,38004,122787,381997,1151458,3376968,
%T A073376 9671284,27123292,74669472,202181112,539342181,1419492627,3690464106,
%U A073376 9487902396,24143758254,60861096714
%N A073376 Sixth convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n>=0, with itself.
%H A073376 G. C. Greubel, <a href="/A073376/b073376.txt">Table of n, a(n) for n = 0..1000</a>
%H A073376 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (7,-7,-49,91,161,-357,-363,714,644,-728,-784,224, 448,128).
%F A073376 a(n) = Sum_{k=0..n} b(k) * c(n-k), with b(k) = A001045(k+1) and c(k) = A073375(k).
%F A073376 a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+6, 6) * binomial(n-k, k) * 2^k.
%F A073376 a(n) = ((1+n)*(4884880 +4449396*n +1525272*n^2 +247653*n^3 +19152*n^4 +567*n^5)* U(n+1) + 2*(2+n)*(2321720 +2182242*n +765993*n^2 +126621*n^3 +9927*n^4 +297*n^5 )*U(n))/(6!*3^9) with U(n) = A001045(n+1), n>=0.
%F A073376 G.f.: 1/(1-(1+2*x)*x)^7 = 1/((1+x)*(1-2*x))^7.
%F A073376 E.g.f.: (1/(6!*3^10))*( 4096*(9305 +56535*x +83745*x^2 +47700*x^3 +12060*x^4 +1350*x^5 +54*x^6)*exp(2*x) + (4402000 -5784960*x +2454120*x^2 -457920*x^3 +41130*x^4 -1728*x^5 +27*x^6)*exp(-x)). - _G. C. Greubel_, Sep 29 2022
%t A073376 Table[(2^(n+7)*(297760 +500640*n +302778*n^2 +87255*n^3 +12915*n^4 +945*n^5 +27*n^6) +(-1)^n*(4402000 +4038132*n +1453788*n^2 +265545*n^3 +26145*n^4 +1323*n^5 +27*n^6))/(6!*3^10), {n,0,40}] (* _G. C. Greubel_, Sep 29 2022 *)
%o A073376 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1+x)*(1-2*x))^7 )); // _G. C. Greubel_, Sep 29 2022
%o A073376 (SageMath)
%o A073376 def A073376(n): return (2^(n+7)*(297760 +500640*n +302778*n^2 +87255*n^3 +12915*n^4 +945*n^5 +27*n^6) +(-1)^n*(4402000 +4038132*n +1453788*n^2 +265545*n^3 +26145*n^4 +1323*n^5 +27*n^6))/(factorial(6)*3^10)
%o A073376 [A073376(n) for n in range(40)] # _G. C. Greubel_, Sep 29 2022
%Y A073376 Seventh (m=6) column of triangle A073370.
%Y A073376 Cf. A001045, A073375.
%K A073376 nonn,easy
%O A073376 0,2
%A A073376 _Wolfdieter Lang_, Aug 02 2002