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%I #18 Apr 02 2020 19:31:28
%S 1,1,1,7,10,7,17,103,103,17,203,2948,7138,2948,203,583,20091,100286,
%T 100286,20091,583,3491,261462,2511213,5092148,2511213,261462,3491,
%U 10481,1670771,29075841,107621147,107621147,29075841,1670771,10481,254963
%N Triangle read by rows of operator ordering coefficients corresponding to the Legendre polynomials L_n(x).
%H T. Amdeberhan, V. de Angelis, A. Dixit, V. H. Moll and C. Vignat, <a href="http://dauns01.math.tulane.edu/~vhm/papers_html/ordering1.pdf">From sequences to polynomials and back, via operator orderings</a>, 2013.
%H Carl M. Bender and Gerald V. Dunne, <a href="http://dx.doi.org/10.1063/1.527869">Polynomials and operator orderings</a>, J. Math. Phys. 29 (1988), 1727-1731.
%e Triangle begins:
%e 1
%e 1,1
%e 7,10,7
%e 17,103,103,17
%e 203,2948,7138,2948,203
%e 583,20091,100286,100286,20091,583
%e ...
%p A225694F := proc(n,k)
%p add((-1)^(n-k-j)*binomial(n+1,n-k-j)*orthopoly[P](n,I*(j+1/2)),j=0..n-k) ;
%p %/I^n/n! ;
%p expand(%) ;
%p end proc:
%p A225694 := proc(n,k)
%p A225694F(n,k) *denom(A225694F(n,0)) ;
%p end proc:
%p seq(seq( A225694(n,k),k=0..n),n=0..10) ; # _R. J. Mathar_, May 23 2014
%t 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 T[n_, k_] := F[n, k] LCM @@ Denominator[Table[F[n, j], {j, 0, n}]];
%t Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Apr 02 2020, after _R. J. Mathar_ *)
%K nonn,tabl
%O 0,4
%A _N. J. A. Sloane_, May 27 2013
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