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 A383651 #22 May 04 2025 14:43:33
%S A383651 1,3,31,135,1015,5271,34903,196311,1230295,7172055,43871191,259871703,
%T A383651 1572651991,9382224855,56508097495,338189591511,2032573522903,
%U A383651 12181697242071,73145159033815,438651051877335,2632785920566231,15793197086188503,94773256265966551
%N A383651 Expansion of 1/((1-x) * (1+4*x) * (1-6*x)).
%H A383651 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,22,-24).
%F A383651 a(n) = Sum_{k=0..n} 5^k * (-4)^(n-k) * binomial(n+2,k+2) * Stirling2(k+2,2).
%F A383651 a(n) = Sum_{k=0..n} (-5)^k * 6^(n-k) * binomial(n+2,k+2) * Stirling2(k+2,2).
%F A383651 a(n) = (6^(n+2) - 2 + (-4)^(n+2))/50 = (A083578(n+2) - 1)/25.
%F A383651 a(n) = 3*a(n-1) + 22*a(n-2) - 24*a(n-3).
%F A383651 E.g.f.: exp(-4*x)*(8 - exp(5*x) + 18*exp(10*x))/25. - _Stefano Spezia_, May 04 2025
%o A383651 (PARI) a(n) = (6^(n+2)-2+(-4)^(n+2))/50;
%Y A383651 Cf. A051958, A083578.
%K A383651 nonn,easy
%O A383651 0,2
%A A383651 _Seiichi Manyama_, May 04 2025