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 A016223 #41 May 03 2025 10:19:15
%S A016223 1,12,105,820,6081,43932,312985,2212740,15576561,109385452,767096265,
%T A016223 5375266260,37649233441,263634112572,1845796701945,12922008569380,
%U A016223 90459786608721,633241412753292,4432781515242025,31029837110570100,217210325789494401,1520478144588475612
%N A016223 Expansion of 1/((1-x) * (1-4*x) * (1-7*x)).
%H A016223 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12, -39, 28).
%F A016223 a(n) = (1/18) - (16/9)*4^n + (49/18)*7^n. - _Antonio Alberto Olivares_, Feb 07 2010 [corrected by _Seiichi Manyama_, May 03 2025]
%F A016223 a(0)=1, a(1)=12, a(n) = 11*a(n-1) - 28*a(n-2) + 1. - _Vincenzo Librandi_, Feb 10 2011
%F A016223 E.g.f.: exp(x)*(1 - 32*exp(3*x) + 49*exp(6*x))/(2!*3^2). - This is (d^2/dx^2) (exp(x)*(exp(x) - 1)^2 / (2*3^2)). See also the second column of the Sheffer triangle A282629 divided by 3^2. - _Wolfdieter Lang_, Apr 08 2017
%F A016223 From _Seiichi Manyama_, May 03 2025: (Start)
%F A016223 a(n) = Sum_{k=0..n} 3^k * binomial(n+2,k+2) * Stirling2(k+2,2).
%F A016223 G.f.: B(x)^3, where B(x) is the g.f. of A383627. (End)
%p A016223 a:=n->sum((7^(n+1-j)-4^(n+1-j))/3, j=0..n+1): seq(a(n), n=0..20); # _Zerinvary Lajos_, Jan 15 2007
%o A016223 (PARI) a(n) = (1-2*4^(n+2)+7^(n+2))/18; \\ _Seiichi Manyama_, May 03 2025
%Y A016223 Cf. A002450, A021874, A111577.
%Y A016223 Cf. A282629, A383627.
%K A016223 nonn,easy
%O A016223 0,2
%A A016223 _N. J. A. Sloane_