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 A128210 Number triangle T(n,k)=(-1)^(n-k)*[k<=n]*Product{i=1..n,Sum{j=0..i-1,A078008(j-1)}/Product{i=1..k,Sum{j=0..i-1,A078008(j-1)}}. 1

%I

%S 1,-1,1,1,-1,1,-3,3,-3,1,15,-15,15,-5,1,-165,165,-165,55,-11,1,3465,

%T -3465,3465,-1155,231,-21,1,-148995,148995,-148995,49665,-9933,903,

%U -43,1,12664575,-12664575,12664575

%N Number triangle T(n,k)=(-1)^(n-k)*[k<=n]*Product{i=1..n,Sum{j=0..i-1,A078008(j-1)}/Product{i=1..k,Sum{j=0..i-1,A078008(j-1)}}.

%C Inverse is A128208. Sub-diagonals include -A001045(n+1) and A084175(n+1).

%e Triangle begins

%e 1,

%e -1, 1,

%e 1, -1, 1,

%e -3, 3, -3, 1,

%e 15, -15, 15, -5, 1,

%e -165, 165, -165, 55, -11, 1,

%e 3465, -3465, 3465, -1155, 231, -21, 1,

%e -148995, 148995, -148995, 49665, -9933, 903, -43, 1

%K easy,sign,tabl

%O 0,7

%A _Paul Barry_, Feb 19 2007

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Last modified May 17 05:13 EDT 2021. Contains 343965 sequences. (Running on oeis4.)