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A055373 Invert transform applied twice to Pascal's triangle A007318. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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 (kolotoko(aT)lagoon.nc), 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

a(n, k)=3^(n-1)*C(n, k).

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

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.

Sequence in context: A065231 A019918 A260303 * A263333 A134440 A129529

Adjacent sequences:  A055370 A055371 A055372 * A055374 A055375 A055376

KEYWORD

nonn,tabl

AUTHOR

Christian G. Bower, May 16 2000

STATUS

approved

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Last modified March 26 14:18 EDT 2019. Contains 321497 sequences. (Running on oeis4.)