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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

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 February 22 09:22 EST 2020. Contains 332133 sequences. (Running on oeis4.)