A164976 - OEIS

%I #26 Oct 15 2023 14:26:35

%S 1,1,2,0,5,4,-1,4,16,8,-1,-3,25,44,16,0,-10,7,102,112,32,1,-8,-41,97,

%T 344,272,64,1,4,-74,-80,528,1040,640,128,0,15,-33,-366,121,2168,2928,

%U 1472,256,-1,12,75,-426,-1219,1898,7664,7840,3328,512

%N Triangle read by rows, expansion of 1/(1-2*y*x-x+x^2-y*x^2).

%C Leftmost column is A010892.

%C Rows sum up to A000244 and diagonals to A000073.

%C A164975 has a similar g.f.: x/(1-2*y*x-x-x^2+y*x^2).. - _Georg Fischer_, Oct 15 2023

%H Georg Fischer, <a href="/A164976/b164976.txt">Table of n, a(n) for n = 1..5050</a>

%e Triangle begins:

%e    1;

%e    1,   2;

%e    0,   5,   4;

%e   -1,   4,  16,   8;

%e   -1,  -3,  25,  44,  16;

%e    0, -10,   7, 102, 112,  32;

%e    1,  -8, -41,  97, 344, 272, 64;

%e   ...

%p s := 1/(1-2*y*x-x+x^2-y*x^2): t := series(s, x, 12):

%p seq(print(seq(coeff(coeff(t, x, n), y, m), m=0..n)), n=0..11); # _Georg Fischer_, Oct 15 2023

%Y Cf. A164975, A000244, A000045, A164965, A000073.

%Y Cf. A010892  (1st column), A000079 (right diagonal).

%K tabl,sign

%O 0,3

%A _Mark Dols_, Sep 03 2009

%E Missing commas inserted in what used to be the term "1-8-41" (now "1,-8,-41") by Geoff Bailey (geoff(AT)maths.usyd.edu.au), Nov 30 2009

%E Definition changed by _Georg Fischer_, Oct 15 2023