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T(i,j) = (-1)^(i+j)*(i+1)*binomial(i,j)*2^(i-j)*4^j.
0

%I #23 Apr 28 2022 12:19:31

%S 1,-4,8,12,-48,48,-32,192,-384,256,80,-640,1920,-2560,1280,-192,1920,

%T -7680,15360,-15360,6144,448,-5376,26880,-71680,107520,-86016,28672,

%U -1024,14336,-86016,286720,-573440,688128,-458752,131072,2304,-36864,258048,-1032192,2580480,-4128768,4128768,-2359296,589824

%N T(i,j) = (-1)^(i+j)*(i+1)*binomial(i,j)*2^(i-j)*4^j.

%C Apart from signs, row i equals (i+1) times row i of A038210. - _Joerg Arndt_, Aug 07 2020

%e Triangle starts:

%e 1,

%e -4, 8,

%e 12, -48, 48,

%e -32, 192, -384, 256,

%e 80, -640, 1920, -2560, 1280,

%e -192, 1920, -7680, 15360, -15360, 6144,

%e 448, -5376, 26880, -71680, 107520, -86016, 28672,

%e -1024, 14336, -86016, 286720, -573440, 688128, -458752, 131072,...

%o (PARI) T(i,j) = (-1)^(i+j)*(i+1)*binomial(i,j)*2^(i-j)*4^j;

%o for(i=0,10,for(j=0,i,print1(T(i,j),", "));print()); \\ _Joerg Arndt_, Aug 07 2020

%K tabl,easy,sign

%O 0,2

%A _Roger L. Bagula_, Apr 07 2008

%E Corrected and edited by _Joerg Arndt_, Aug 07 2020

%E Definition corrected to match terms by _Georg Fischer_, Apr 28 2022