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 A155866 #20 Dec 23 2024 11:38:05
%S A155866 1,2,6,22,91,413,2032,10754,60832,365815,2327835,15612872,109992442,
%T A155866 811500784,6253327841,50211976959,419239644142,3632891419054,
%U A155866 32616077413970,302915722319509,2906047810600157,28761123170398258,293296874302640254,3078390856651377534,33220524976632438215
%N A155866 A 'Morgan Voyce' transform of the Bell numbers A000110.
%C A155866 Image of Bell numbers under Riordan array (1/(1-x), x/(1-x)^2).
%H A155866 G. C. Greubel, <a href="/A155866/b155866.txt">Table of n, a(n) for n = 0..550</a>
%H A155866 Veronica Bitonti, Bishal Deb, and Alan D. Sokal, <a href="https://arxiv.org/abs/2412.10214">Thron-type continued fractions (T-fractions) for some classes of increasing trees</a>, arXiv:2412.10214 [math.CO], 2024. See p. 58.
%F A155866 G.f.: 1/(1 -x -x/(1 -x -x/(1 -x -x/(1 -x -2*x/(1 -x -x/(1 -x -3*x/(1 -x -x/(1 -x -4*x/(1 - ... (continued fraction).
%F A155866 a(n) = Sum_{k=0..n} binomial(n+k,2k)*A000110(k).
%F A155866 a(n) = Sum_{k=0..n} A085478(n,k)*A000110(k). - _Philippe Deléham_, Jan 31 2009
%t A155866 A155866[n_]:= Sum[Binomial[n+j, 2*j]*BellB[j], {j,0,n}];
%t A155866 Table[A155866[n], {n, 0, 30}] (* _G. C. Greubel_, Jun 10 2021 *)
%o A155866 (Magma) [(&+[Binomial(n+j,2*j)*Bell(j): j in [0..n]]): n in [0..30]]; // _G. C. Greubel_, Jun 10 2021
%o A155866 (Sage)
%o A155866 def A155866(n): return sum( binomial(n+j, 2*j)*bell_number(j) for j in (0..n) )
%o A155866 [A155866(n) for n in (0..30)] # _G. C. Greubel_, Jun 10 2021
%Y A155866 Cf. A000110, A085478.
%K A155866 easy,nonn
%O A155866 0,2
%A A155866 _Paul Barry_, Jan 29 2009