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 A073397 #17 Aug 20 2024 23:16:30 %S A073397 1,18,198,1680,12060,76824,446952,2420352,12363120,60151520,280833696, %T A073397 1265442048,5528697408,23507763840,97575960960,396398370816, %U A073397 1579498956288,6184543546368,23833455191040,90522348871680,339263015528448,1255995653197824,4597442198728704 %N A073397 Eighth convolution of A002605(n) (generalized (2,2)-Fibonacci), n>=0, with itself. %C A073397 For a(n) in terms of U(n+1) and U(n), with U(n) = A002605(n), see A073387 and the row polynomials of triangles A073405 and A073406. %H A073397 G. C. Greubel, <a href="/A073397/b073397.txt">Table of n, a(n) for n = 0..1000</a> %H A073397 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (18,-126,384,-144,-2016,3360,4608,-12384,-8512, 24768,18432,-26880,-32256,4608,24576,16128,4608,512). %F A073397 a(n) = Sum_{k=0..n} b(k)*c(n-k), with b(k) = A002605(k) and c(k) = A073394(k). %F A073397 a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+8, 8)*binomial(n-k, k)*2^(n-k). %F A073397 G.f.: 1/(1-2*x*(1+x))^9. %t A073397 CoefficientList[Series[1/(1-2*x-2*x^2)^9, {x,0,30}], x] (* _G. C. Greubel_, Oct 06 2022 *) %o A073397 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1/(1-2*x-2*x^2)^9 )); // _G. C. Greubel_, Oct 06 2022 %o A073397 (SageMath) %o A073397 def A073397_list(prec): %o A073397 P.<x> = PowerSeriesRing(ZZ, prec) %o A073397 return P( 1/(1-2*x-2*x^2)^9 ).list() %o A073397 A073397_list(30) # _G. C. Greubel_, Oct 06 2022 %Y A073397 Ninth (m=8) column of triangle A073387. %Y A073397 Cf. A002605, A073387, A073394, A073405, A073406. %K A073397 nonn,easy %O A073397 0,2 %A A073397 _Wolfdieter Lang_, Aug 02 2002