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A225694
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Triangle read by rows of operator ordering coefficients corresponding to the Legendre polynomials L_n(x).
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2
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1, 1, 1, 7, 10, 7, 17, 103, 103, 17, 203, 2948, 7138, 2948, 203, 583, 20091, 100286, 100286, 20091, 583, 3491, 261462, 2511213, 5092148, 2511213, 261462, 3491, 10481, 1670771, 29075841, 107621147, 107621147, 29075841, 1670771, 10481, 254963
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table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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LINKS
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EXAMPLE
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Triangle begins:
1
1,1
7,10,7
17,103,103,17
203,2948,7138,2948,203
583,20091,100286,100286,20091,583
...
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MAPLE
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A225694F := proc(n, k)
add((-1)^(n-k-j)*binomial(n+1, n-k-j)*orthopoly[P](n, I*(j+1/2)), j=0..n-k) ;
%/I^n/n! ;
expand(%) ;
end proc:
A225694F(n, k) *denom(A225694F(n, 0)) ;
end proc:
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MATHEMATICA
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F[n_, k_] := F[n, k] = Sum[(-1)^(n - k - j) Binomial[n + 1, n - k - j]* LegendreP[n, I(j + 1/2)], {j, 0, n - k}] /I^n/n!;
T[n_, k_] := F[n, k] LCM @@ Denominator[Table[F[n, j], {j, 0, 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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