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1, 1, 1, 1, 0, 1, 1, 13, 13, 1, 1, 25, 38, 25, 1, 1, -185, -160, -160, -185, 1, 1, -779, -964, -952, -964, -779, 1, 1, 7497, 6718, 6520, 6520, 6718, 7497, 1, 1, 45907, 53404, 52612, 52402, 52612, 53404, 45907, 1, 1, -524629, -478722, -471238, -472042, -472042, -471238, -478722, -524629, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,8
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COMMENTS
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Row sums are {1, 2, 2, 28, 90, -688, -4436, 41472, 356250, -3893260, -41666708, ...}.
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LINKS
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FORMULA
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T(n,k) = T(n,n-k).
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EXAMPLE
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Triangle begins as:
1;
1, 1;
1, 0, 1;
1, 13, 13, 1;
1, 25, 38, 25, 1;
1, -185, -160, -160, -185, 1;
1, -779, -964, -952, -964, -779, 1;
1, 7497, 6718, 6520, 6520, 6718, 7497, 1;
1, 45907, 53404, 52612, 52402, 52612, 53404, 45907, 1;
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MAPLE
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if n = 0 then
0;
else
(-1)^n*n*procname(n-1)-1 ;
end if;
end proc:
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MATHEMATICA
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b[n_]:= b[n] = If[n==0, 0, (-1)^n*n*b[n-1] -1];
T[n_, k_]:= T[n, k] = 1 - (b[k] +b[n-k] -b[n]);
Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten
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PROG
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(PARI) b(n) = if(n==0, 0, (-1)^n*n*b(n-1) -1);
T(n, k) = 1 + b(n) - b(k) - b(n-k); \\ G. C. Greubel, Nov 26 2019
(Magma)
function b(n)
if n eq 0 then return 0;
else return (-1)^n*n*b(n-1) -1;
end if; return b; end function;
[1+b(n)-b(k)-b(n-k): k in [0..n], n in [1..10]]; // G. C. Greubel, Nov 26 2019
(Sage)
@CachedFunction
def b(n):
if (n==0): return 0
else: return (-1)^n*n*b(n-1) -1
[[1+b(n)-b(k)-b(n-k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Nov 26 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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