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 A112498 #5 Jul 08 2025 12:05:01 %S A112498 3,29,164,726,2805,9975,33630,109424,347519,1085313,3349848,10253994, %T A112498 31203945,94561643,285716018,861472836,2593592883,7800176565, %U A112498 23441423340,70410252350,211411111133,634610819679,1904620987014 %N A112498 Third column of second-order Eulerian triangle A008517 divided by 2. %C A112498 See A004301 for the doubled sequence. %H A112498 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (10,-40,82,-91,52,-12). %F A112498 a(n)=A008517(n, 3)/2. %F A112498 G.f.: x^3*(3-x-6*x^2)/(((1-x)^3)*((1-2*x)^2)*(1-3*x)). See the comment on column g.f.s under A008517. %F A112498 a(n) = 3*a(n-1) + (2*n-3)*(2^(n-1)-n), n>3, with a(3)=3. %F A112498 a(n)= 3*A112502(n-3) - A112502(n-4) - 6*A112502(n-5), n>=5. %Y A112498 Cf. A000295 (one half of second column). %K A112498 nonn,easy %O A112498 3,1 %A A112498 _Wolfdieter Lang_, Oct 14 2005