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%I #13 Sep 08 2022 08:45:41
%S 1,2,6,22,91,413,2032,10754,60832,365815,2327835,15612872,109992442,
%T 811500784,6253327841,50211976959,419239644142,3632891419054,
%U 32616077413970,302915722319509,2906047810600157,28761123170398258
%N A 'Morgan Voyce' transform of the Bell numbers A000110.
%C Image of Bell numbers under Riordan array (1/(1-x), x/(1-x)^2).
%H G. C. Greubel, <a href="/A155866/b155866.txt">Table of n, a(n) for n = 0..550</a>
%F 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 a(n) = Sum_{k=0..n} binomial(n+k,2k)*A000110(k).
%F a(n) = Sum_{k=0..n} A085478(n,k)*A000110(k). - _Philippe Deléham_, Jan 31 2009
%t A155866[n_]:= Sum[Binomial[n+j, 2*j]*BellB[j], {j,0,n}];
%t Table[A155866[n], {n, 0, 30}] (* _G. C. Greubel_, Jun 10 2021 *)
%o (Magma) [(&+[Binomial(n+j,2*j)*Bell(j): j in [0..n]]): n in [0..30]]; // _G. C. Greubel_, Jun 10 2021
%o (Sage)
%o def A155866(n): return sum( binomial(n+j, 2*j)*bell_number(j) for j in (0..n) )
%o [A155866(n) for n in (0..30)] # _G. C. Greubel_, Jun 10 2021
%Y Cf. A000110, A085478.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Jan 29 2009
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