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A171274
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Matrix inverse of A142458.
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1
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1, -1, 1, 7, -8, 1, -235, 273, -39, 1, 35353, -41116, 5928, -166, 1, -22683409, 26382125, -3804940, 106900, -677, 1, 60147266239, -69954818244, 10089231945, -283474190, 1796973, -2724, 1, -648088191536203, 753764796604717, -108711714513099, 3054442698125, -19362601277, 29358651, -10915, 1
(list;
table;
graph;
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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FORMULA
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Sum_{j=k..n} T(n,j)*A142458(j,k) = delta(n,k), the Kronecker delta.
T(n, k) = (-1)*Sum_{j=k+1..n} T(n, j)*A142458(j, k), with T(n, n) = 1. - R. J. Mathar, Jun 04 2011
Sum_{k=1..n} T(n, k) = 0^(n-1).
T(n, n-1) = (-1)*A142458(n, 2). (End)
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EXAMPLE
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The triangle starts as:
1;
-1, 1;
7, -8, 1;
-235, 273, -39, 1;
35353, -41116, 5928, -166, 1;
-22683409, 26382125, -3804940, 106900, -677, 1;
60147266239, -69954818244, 10089231945, -283474190, 1796973, -2724, 1;
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MAPLE
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A142458:= proc(n, k) if n = k then 1; elif k > n or k < 1 then 0 ; else (3*n-3*k+1)*procname(n-1, k-1)+(3*k-2)*procname(n-1, k) ; end if; end proc:
A171274 := proc(n, k) option remember; if k=n then 1; else -add( procname(n, j)*A142458(j, k), j=k+1..n); end if; end proc:
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MATHEMATICA
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T[n_, k_, m_]:= T[n, k, m]= If[k==1 || k==n, 1, (m*n-m*k+1)*T[n-1, k-1, m] + (m*k -m+1)*T[n-1, k, m]];
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PROG
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(Sage)
def T(n, k, m):
if (k==1 or k==n): return 1
else: return (m*(n-k)+1)*T(n-1, k-1, m) + (m*k-m+1)*T(n-1, k, m)
def A142458(n, k): return T(n, k, 3)
@CachedFunction
if (k==n): return 1
else: return (-1)*sum( A171274(n, j)*A142458(j, k) for j in (k+1..n) )
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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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