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 A081907 #22 Mar 22 2025 15:13:07
%S A081907 1,8,61,450,3240,22896,159408,1096416,7464960,50388480,337602816,
%T A081907 2247326208,14874679296,97955205120,642150789120,4192482779136,
%U A081907 27270729105408,176789554200576,1142549512519680,7363096858460160,47326939807481856,303461150525227008,1941420131673440256
%N A081907 Fifth binomial transform of binomial(n+2, 2).
%C A081907 Binomial transform of A081894.
%C A081907 6th binomial transform of (1,2,1,0,0,0,...).
%H A081907 G. C. Greubel, <a href="/A081907/b081907.txt">Table of n, a(n) for n = 0..1000</a>
%H A081907 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (18,-108,216).
%F A081907 a(n) = 6^n*(n^2 + 23*n + 72)/72.
%F A081907 G.f.: (1-5*x)^2/(1-6*x)^3.
%F A081907 E.g.f.: (2 + 4*x + x^2)*exp(6*x)/2. - _G. C. Greubel_, Oct 17 2018
%p A081907 seq(coeff(series((1-5*x)^2/(1-6*x)^3,x,n+1), x, n), n = 0 .. 20); # _Muniru A Asiru_, Oct 18 2018
%t A081907 Table[6^n*(n^2+23*n+72)/72, {n,0,50}] (* or *) LinearRecurrence[{18,-108, 216}, {1, 8, 61}, 50] (* _G. C. Greubel_, Oct 17 2018 *)
%o A081907 (PARI) vector(50, n, n--; 6^n*(n^2 +23*n +72)/72) \\ _G. C. Greubel_, Oct 17 2018
%o A081907 (Magma) [6^n*(n^2 +23*n +72)/72: n in [0..50]]; // _G. C. Greubel_, Oct 17 2018
%o A081907 (GAP) List([1..20],n->6^(n-1)*(n^2+21*n+50))/72; # _Muniru A Asiru_, Oct 18 2018
%Y A081907 Cf. A000217, A081894.
%K A081907 easy,nonn
%O A081907 0,2
%A A081907 _Paul Barry_, Mar 30 2003