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 A385898 #13 Jul 29 2025 21:34:27
%S A385898 1,272,2763,13024,42125,108576,240247,476288,869049,1486000,2411651,
%T A385898 3749472,5623813,8181824,11595375,16062976,21811697,29099088,38215099,
%U A385898 49484000,63266301,79960672,100005863,123882624,152115625,185275376,223980147,268897888,320748149
%N A385898 a(n) = 16*n^5 + 70*n^4 + 105*n^3 + 65*n^2 + 15*n + 1.
%H A385898 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A385898 a(n) = [x^n] (x^4 + 506*x^3 + 1146*x^2 + 266*x + 1)/(x - 1)^6.
%F A385898 a(n) = 6! * [x^6] (1 - sin(n*x))^(-1/n) for n > 0.
%F A385898 a(n) = A385896(n + 6, 6).
%F A385898 gcd(a(n), a(n+1)) = 1.
%p A385898 gf := (x^4 + 506*x^3 + 1146*x^2 + 266*x + 1)/(x - 1)^6:
%p A385898 ser := series(gf, x, 30): seq(coeff(ser, x, n), n = 0..28);
%t A385898 a[n_]:=16n^5+70n^4+105n^3+65n^2+15n+1;Array[a,29,0] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{1, 272, 2763, 13024, 42125, 108576},29] (* or *) CoefficientList[Series[ (x^4 + 506*x^3 + 1146*x^2 + 266*x + 1)/(x - 1)^6,{x,0,28}],x] (* _James C. McMahon_, Jul 24 2025 *)
%Y A385898 Cf. A385896 (column 6).
%K A385898 nonn,easy
%O A385898 0,2
%A A385898 _Peter Luschny_, Jul 21 2025