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 A055373 #34 Jan 19 2023 05:21:39
%S A055373 1,1,1,3,6,3,9,27,27,9,27,108,162,108,27,81,405,810,810,405,81,243,
%T A055373 1458,3645,4860,3645,1458,243,729,5103,15309,25515,25515,15309,5103,
%U A055373 729,2187,17496,61236,122472,153090,122472,61236,17496,2187,6561
%N A055373 Invert transform applied twice to Pascal's triangle A007318.
%C A055373 Triangle T(n,k), 0 <= k <= n, read by rows, given by [1, 2, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 2, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938. - _Philippe Deléham_, Aug 10 2005
%C A055373 T(n,k) is the number of sequences of nonempty sequences of nonempty bit strings with n bits and exactly k 1's over all strings in the sequence of sequences. In other words, these are sequences of the structures counted by A055372. - _Geoffrey Critzer_, Apr 06 2013
%H A055373 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A055373 <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>
%F A055373 T(n,k) = 3^(n-1)*C(n, k) for n > 0.
%F A055373 O.g.f.: 1/(2 - A(x,y)) where A(x,y) is the o.g.f. for A055372. - _Geoffrey Critzer_, Apr 06 2013
%e A055373 Triangle begins:
%e A055373 1;
%e A055373 1, 1;
%e A055373 3, 6, 3;
%e A055373 9, 27, 27, 9;
%e A055373 27, 108, 162, 108, 27;
%e A055373 ...
%t A055373 nn=10;f[list_]:=Select[list,#>0&];a=(x+y x)/(1-(x+y x));b=1/(1-a);Map[f,CoefficientList[Series[1/(2-b),{x,0,nn}],{x,y}]]//Grid (* _Geoffrey Critzer_, Apr 06 2013 *)
%Y A055373 Cf. A000244, A007318, A055372, A055374.
%Y A055373 Cf. A084938.
%K A055373 nonn,tabl
%O A055373 0,4
%A A055373 _Christian G. Bower_, May 16 2000