login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A171636 Coefficients of Lommel polynomials:n=m;p(x,n,m)=(Gamma[n + m]/(Gamma[n] ((z/ 2))^m)) HypergeometricPFQ[{((1 - m))/2, (-m)/2}, {n, (-m), 1 - n - m}, z^2] 0

%I

%S 2,24,0,1,480,0,16,13440,0,360,0,1,483840,0,10752,0,42,21288960,0,

%T 403200,0,1728,0,1,1107025920,0,18247680,0,79200,0,80,66421555200,0,

%U 968647680,0,4118400,0,5280,0,1,4516665753600,0,59041382400,0,242161920

%N Coefficients of Lommel polynomials:n=m;p(x,n,m)=(Gamma[n + m]/(Gamma[n] ((z/ 2))^m)) HypergeometricPFQ[{((1 - m))/2, (-m)/2}, {n, (-m), 1 - n - m}, z^2]

%C Row sums are: 2, 25, 496, 13801, 494634, 21693889, 1125352880, 67394326561, 4575949647490, 347347588935481

%H Weisstein, Eric W. <a href="http://mathworld.wolfram.com/LommelPolynomial.html">Lommel Polynomial</a>. MathWorld.

%F n=m;p(x,n,m)=(Gamma[n + m]/(Gamma[n] ((z/ 2))^m)) HypergeometricPFQ[{((1 - m))/2, (-m)/2}, {n, (-m), 1 - n - m}, z^2]

%e {2},

%e {24, 0, 1},

%e {480, 0, 16},

%e {13440, 0, 360, 0, 1},

%e {483840, 0, 10752, 0, 42},

%e {21288960, 0, 403200, 0, 1728, 0, 1},

%e {1107025920, 0, 18247680, 0, 79200, 0, 80},

%e {66421555200, 0, 968647680, 0, 4118400, 0, 5280, 0, 1},

%e {4516665753600, 0, 59041382400, 0, 242161920, 0, 349440, 0, 130},

%e {343266597273600, 0, 4064999178240, 0, 15968010240, 0, 24460800, 0, 12600, 0, 1}

%t LommelR1[m_, n_, z_] := (Gamma[n + m]/(Gamma[n] ((z/ 2))^m)) HypergeometricPFQ[{((1 - m))/2, (- m)/2}, {n, (-m), 1 - n - m}, z^2]

%t Table[CoefficientList[Expand[LommelR1[n, n, x]*x^n], x], {n, 1, 10}]

%t Flatten[%]

%K nonn,uned,tabl

%O 1,1

%A _Roger L. Bagula_, Dec 13 2009

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 19 09:45 EST 2021. Contains 340269 sequences. (Running on oeis4.)