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A055372 Invert transform of Pascal's triangle A007318. 14
1, 1, 1, 2, 4, 2, 4, 12, 12, 4, 8, 32, 48, 32, 8, 16, 80, 160, 160, 80, 16, 32, 192, 480, 640, 480, 192, 32, 64, 448, 1344, 2240, 2240, 1344, 448, 64, 128, 1024, 3584, 7168, 8960, 7168, 3584, 1024, 128, 256, 2304, 9216, 21504, 32256, 32256, 21504, 9216, 2304, 256 (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, 1, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 1, 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 nonempty bit strings with n bits and exactly k 1's over all strings in the sequence. For example, T(2,1)=4 because we have {(01)},{(10)},{(0),(1)},{(1),(0)}. - Geoffrey Critzer, Apr 06 2013
LINKS
N. J. A. Sloane, Transforms
FORMULA
a(n,k) = 2^(n-1)*C(n, k), for n>0.
G.f.: A(x, y)=(1-x-xy)/(1-2x-2xy).
As an infinite lower triangular matrix, equals A134309 * A007318. - Gary W. Adamson, Oct 19 2007
Sum_{k=0..n} T(n,k)*x^k = A000007(n), A011782(n), A081294(n), A081341(n), A092811(n), A093143(n), A067419(n) for x = -1, 0, 1, 2, 3, 4, 5 respectively. - Philippe Deléham, Feb 05 2012
EXAMPLE
Triangle begins:
1;
1, 1;
2, 4, 2;
4, 12, 12, 4;
8, 32, 48, 32, 8;
...
MATHEMATICA
nn=10; f[list_]:=Select[list, #>0&]; a=(x+y x)/(1-(x+y x)); Map[f, CoefficientList[Series[1/(1-a), {x, 0, nn}], {x, y}]]//Grid (* Geoffrey Critzer, Apr 06 2013 *)
CROSSREFS
Row sums give A081294. Cf. A000079, A007318, A055373, A055374.
Cf. A134309.
T(2n,n) gives A098402.
Sequence in context: A240893 A241108 A151706 * A241078 A198285 A136620
KEYWORD
nonn,tabl
AUTHOR
Christian G. Bower, May 16 2000
STATUS
approved

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Last modified June 20 09:16 EDT 2024. Contains 373515 sequences. (Running on oeis4.)