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Invert transform applied three times to Pascal's triangle A007318.
2

%I #19 Jan 21 2020 10:25:34

%S 1,1,1,4,8,4,16,48,48,16,64,256,384,256,64,256,1280,2560,2560,1280,

%T 256,1024,6144,15360,20480,15360,6144,1024,4096,28672,86016,143360,

%U 143360,86016,28672,4096,16384,131072,458752,917504,1146880,917504

%N Invert transform applied three times to Pascal's triangle A007318.

%C Triangle T(n,k), 0 <= k <= n, read by rows, given by [1, 3, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 3, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938. - _Philippe Deléham_, Aug 10 2005

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%H <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>

%F a(n,k) = 4^(n-1)*C(n, k), for n>0.

%F G.f.: (-1+3*x+3*x*y)/(-1+4*x+4*x*y). - _R. J. Mathar_, Aug 12 2015

%e 1;

%e 1, 1;

%e 4, 8, 4;

%e 16, 48, 48, 16;

%e 64, 256, 384, 256, 64; ...

%Y Cf. A000302, A007318, A055372, A055373.

%K nonn,tabl,easy

%O 0,4

%A _Christian G. Bower_, May 16 2000