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 A225694 Triangle read by rows of operator ordering coefficients corresponding to the Legendre polynomials L_n(x). 2
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Table of n, a(n) for n=0..36. T. Amdeberhan, V. de Angelis, A. Dixit, V. H. Moll and C. Vignat, From sequences to polynomials and back, via operator orderings, 2013. Carl M. Bender and Gerald V. Dunne, Polynomials and operator orderings, J. Math. Phys. 29 (1988), 1727-1731. EXAMPLE Triangle begins: 1 1,1 7,10,7 17,103,103,17 203,2948,7138,2948,203 583,20091,100286,100286,20091,583 ... MAPLE 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: A225694 := proc(n, k) A225694F(n, k) *denom(A225694F(n, 0)) ; end proc: seq(seq( A225694(n, k), k=0..n), n=0..10) ; # R. J. Mathar, May 23 2014 MATHEMATICA 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}]]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Apr 02 2020, after R. J. Mathar *) CROSSREFS Sequence in context: A266551 A070405 A010730 * A247191 A317336 A079004 Adjacent sequences: A225691 A225692 A225693 * A225695 A225696 A225697 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, May 27 2013 STATUS approved

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Last modified July 18 21:02 EDT 2024. Contains 374388 sequences. (Running on oeis4.)