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 A383635 #21 May 04 2025 14:44:19
%S A383635 1,55,1940,56210,1461495,35567301,829147810,18774611680,416583297845,
%T A383635 9111004217315,197197849460976,4235712944853390,90470493402792595,
%U A383635 1924292232588575905,40801645704191871710,863108809168841357276,18225784176922532902545
%N A383635 Expansion of 1/( Product_{k=0..4} (1 - (5*k+1) * x) ).
%H A383635 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (55,-1085,9185,-30330,22176).
%F A383635 a(n) = Sum_{k=0..n} 5^k * binomial(n+4,k+4) * Stirling2(k+4,4).
%F A383635 a(n) = (21^(n+4) - 4*16^(n+4) + 6*11^(n+4) - 4*6^(n+4) + 1)/15000.
%F A383635 a(n) = 55*a(n-1) - 1085*a(n-2) + 9185*a(n-3) - 30330*a(n-4) + 22176*a(n-5).
%F A383635 G.f.: B(x)^5, where B(x) is the g.f. of A383629.
%F A383635 a(n) = Sum_{k=0..n} (-5)^k * 21^(n-k) * binomial(n+4,k+4) * Stirling2(k+4,4).
%o A383635 (PARI) a(n) = (21^(n+4)-4*16^(n+4)+6*11^(n+4)-4*6^(n+4)+1)/15000;
%Y A383635 Cf. A383629.
%K A383635 nonn,easy
%O A383635 0,2
%A A383635 _Seiichi Manyama_, May 03 2025