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A333290
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Irregular triangle read by rows: coefficients b_{r,j} (r>=1, j>=0) arising from an expansion of the partition function.
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2
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1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 0, 2, 0, 0, -1, -1, 1, 1, -1, -1, 0, 0, 1, 1, 1, -1, -1, -1, 0, 0, 1, 1, -1, 1, -1, -1, 0, 0, 1, 0, 2, 0, -1, -1, -1, -1, 0, 2, 0, 1, 0, 0, -1, -1, 1, 1, -1, -1, 0, 0, 1, 0, 1, 1, 0, -1, -1, -2, 0, 0, 0, 2, 1, 1, 0, -1, -1, 0, -1, 0, 0, 1, 1, -1, 1, -1, -1, 0, 0, 1, 0, 1, 0, 1, 0, -1, -2, -1, 0, -1, 1
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listen;
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OFFSET
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1,20
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COMMENTS
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LINKS
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EXAMPLE
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Triangle begins:
1,
1,-1,
1,-1,-1,1,
1,-1,-1,0,1,1,-1,
1,-1,-1,0,0,2,0,0,-1,-1,1,
1,-1,-1,0,0,1,1,1,-1,-1,-1,0,0,1,1,-1,
...
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MAPLE
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if r < 1 then
0 ;
elif r = 1 then
if j= 0 then
1;
else
0 ;
end if;
elif j < r-1 then
procname(r-1, j) ;
else
procname(r-1, j) -procname(r-1, j-r+1) ;;
end if;
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MATHEMATICA
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b[r_, j_] := b[r, j] = Which[r < 1, 0, r == 1, If[j == 0, 1, 0], j < r-1, b[r-1, j], True, b[r-1, j] - b[r-1, j-r+1]];
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CROSSREFS
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KEYWORD
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sign,tabf
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AUTHOR
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STATUS
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approved
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