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A091614
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Matrix inverse of triangle A091613.
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3
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1, -1, 1, -3, 0, 1, -1, -3, 0, 1, 5, -6, -2, 0, 1, 13, -4, -5, -2, 0, 1, 27, 1, -7, -4, -2, 0, 1, 41, 12, -4, -6, -4, -2, 0, 1, 43, 35, 4, -6, -5, -4, -2, 0, 1, 25, 72, 18, 0, -5, -5, -4, -2, 0, 1, -23, 128, 40, 11, -2, -4, -5, -4, -2, 0, 1, -157, 205, 77, 30, 8, -1, -4, -5, -4, -2, 0, 1
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,4
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LINKS
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EXAMPLE
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Triangle begins as:
1;
-1, 1;
-3, 0, 1;
-1, -3, 0, 1;
5, -6, -2, 0, 1;
13, -4, -5, -2, 0, 1;
27, 1, -7, -4, -2, 0, 1;
41, 12, -4, -6, -4, -2, 0, 1;
43, 35, 4, -6, -5, -4, -2, 0, 1;
25, 72, 18, 0, -5, -5, -4, -2, 0, 1;
-23, 128, 40, 11, -2, -4, -5, -4, -2, 0, 1;
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MATHEMATICA
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b[n_, l_, k_]:= b[n, l, k]= If[n==0, 1, Sum[If[i==l, 0, Sum[b[n-i*j, i, k], {j, Min[k, n/i]}]], {i, n}]];
t[n_, k_]:= b[n, 0, k] - b[n, 0, k-1]; (* t = A091613 *)
M:= With[{p = 16}, Table[t[n, k], {n, p}, {k, p}]];
T:= Inverse[M];
Table[T[[n, k]], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Nov 27 2021 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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