A055373 Invert transform applied twice to Pascal's triangle A007318.

1, 1, 1, 3, 6, 3, 9, 27, 27, 9, 27, 108, 162, 108, 27, 81, 405, 810, 810, 405, 81, 243, 1458, 3645, 4860, 3645, 1458, 243, 729, 5103, 15309, 25515, 25515, 15309, 5103, 729, 2187, 17496, 61236, 122472, 153090, 122472, 61236, 17496, 2187, 6561

Offset

0,4

Comments

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

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

Links

Table of n, a(n) for n=0..45.

N. J. A. Sloane, Transforms

Index entries for triangles and arrays related to Pascal's triangle

Formula

T(n,k) = 3^(n-1)*C(n, k) for n > 0.

O.g.f.: 1/(2 - A(x,y)) where A(x,y) is the o.g.f. for A055372. - Geoffrey Critzer, Apr 06 2013

Example

Triangle begins:
   1;
   1,   1;
   3,   6,   3;
   9,  27,  27,   9;
  27, 108, 162, 108,  27;
  ...

Mathematica

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 *)

Crossrefs

Cf. A000244, A007318, A055372, A055374.

Cf. A084938.

Sequence in context: A351102 A019918 A260303 * A263333 A328371 A134440

Adjacent sequences: A055370 A055371 A055372 * A055374 A055375 A055376

Keyword

nonn,tabl

Author

Christian G. Bower, May 16 2000

Status

approved