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 A132124 #30 May 09 2024 18:53:38
%S A132124 0,3,17,50,110,205,343,532,780,1095,1485,1958,2522,3185,3955,4840,
%T A132124 5848,6987,8265,9690,11270,13013,14927,17020,19300,21775,24453,27342,
%U A132124 30450,33785,37355,41168,45232,49555,54145,59010,64158,69597,75335,81380,87740,94423
%N A132124 a(n) = n*(n+1)*(8*n + 1)/6.
%C A132124 Convolution of the sequences (0,3,5,0,0,0,...) and (binomial(n+3, 3)), n >= 0. - _Emeric Deutsch_, Aug 30 2007
%H A132124 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A132124 a(n) = A132121(n,2) for n > 1.
%F A132124 G.f.: x*(3+5*x)/(1-x)^4. - _Emeric Deutsch_, Aug 30 2007
%F A132124 From _Bruno Berselli_, Nov 25 2010: (Start)
%F A132124 a(n) = n*A014105(n) - A016061(n-1), since A016061(n-1) = Sum_{k=0..n-1} A014105(k) (n > 0).
%F A132124 Also a(n) = A002412(n) + A006331(n) = A007585(n) + A002378(n). (End)
%F A132124 Sum_{n>=1} 1/a(n) = 54 - 24*(sqrt(2)+1)*Pi/7 - 24*(sqrt(2)+8)*log(2)/7 + 48*sqrt(2)*log(2-sqrt(2))/7. - _Amiram Eldar_, May 20 2023
%F A132124 E.g.f.: exp(x)*x*(18 + 33*x + 8*x^2)/6. - _Stefano Spezia_, Feb 21 2024
%p A132124 seq((1/6)*n*(n+1)*(8*n+1),n=0..40); # _Emeric Deutsch_, Aug 30 2007
%t A132124 a[n_] := n*(n + 1)*(8*n + 1)/6; Array[a, 42, 0] (* _Amiram Eldar_, May 20 2023 *)
%Y A132124 Cf. A000330, A033994, A132112, A050409.
%Y A132124 Cf. A014105, A016061; A002412, A006331; A007585, A002378.
%Y A132124 Row sums of A069011.
%K A132124 nonn,easy
%O A132124 0,2
%A A132124 _Reinhard Zumkeller_, Aug 12 2007