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 A081913 #11 Sep 08 2022 08:45:09 %S A081913 1,2,4,9,24,72,224,688,2048,5888,16384,44288,116736,301056,761856, %T A081913 1896448,4653056,11272192,27000832,64028672,150470656,350748672, %U A081913 811597824,1865416704,4261412864,9680453632,21877489664,49207574528 %N A081913 a(n) = 2^n*(n^3 - 3n^2 + 2n + 48)/48. %C A081913 Binomial transform of A050407, (starting with 1,1,1,2,5,...). 2nd binomial transform of (1,0,0,1,0,0,0,0,...). Case k=2 where a(n,k) = k^n*(n^3 - 3n^2 + 2n + 6k^3)/(6k^3), with g.f. (1 - 3kx + 3k^2x^2 - (k^3-1)x^3)/(1-kx)^4. %H A081913 Vincenzo Librandi, <a href="/A081913/b081913.txt">Table of n, a(n) for n = 0..225</a> %H A081913 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-24,32,-16). %F A081913 a(n) = 2^n*(n^3 - 3n^2 + 2n + 48)/48. %F A081913 G.f.: (1 - 6x + 12x^2 - 7x^3)/(1-2x)^4. %o A081913 (Magma) [2^n*(n^3-3*n^2+2*n+48)/48: n in [0..40]]; // _Vincenzo Librandi_, Apr 27 2011 %Y A081913 Cf. A081914. %K A081913 easy,nonn %O A081913 0,2 %A A081913 _Paul Barry_, Mar 31 2003