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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A001811 Coefficients of Laguerre polynomials.
(Formerly M5185 N2253)
4

%I M5185 N2253

%S 1,25,450,7350,117600,1905120,31752000,548856000,9879408000,

%T 185513328000,3636061228800,74373979680000,1586644899840000,

%U 35272336619520000,816302647480320000,19645683716026368000,491142092900659200000,12740803704070041600000

%N Coefficients of Laguerre polynomials.

%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 799.

%D C. Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 519.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A001811/b001811.txt">Table of n, a(n) for n = 4..100</a>

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

%H C. Lanczos, <a href="/A002457/a002457.pdf">Applied Analysis</a> (Annotated scans of selected pages)

%H <a href="/index/La#Laguerre">Index entries for sequences related to Laguerre polynomials</a>

%F a(n) = n!*n*(n-1)(n-2)(n-3)/(4!)^2. a(4)=1, a(n+1)=a(n) * (n+1)^2 / (n-3).

%F a(n)=A021009(n, 4), n >= 4. E.g.f.: x^4/(4!*(1-x)^5).

%F If we define f(n,i,x)= sum(sum(binomial(k,j)*stirling1(n,k)*stirling2(j,i)*x^(k-j),j=i..k),k=i..n) then a(n)=(-1)^n*f(n,4,-5), (n>=4). - _Milan Janjic_, Mar 01 2009

%e G.f. = x^4 + 25*x^5 + 450*x^6 + 7350*x^7 + 117600*x^8 + 1905120*x^9 + ...

%p with(combstruct):ZL:=[st, {st=Prod(left, right), left=Set(U, card=r+2), right=Set(U, card<r), U=Sequence(Z, card>=1)}, labeled]: subs(r=2, stack): seq(count(subs(r=2, ZL), size=m), m=4..19) ; # _Zerinvary Lajos_, Feb 07 2008

%t Table[n! n (n - 1) (n - 2) (n - 3)/(4!)^2, {n, 4, 20}] (* _T. D. Noe_, Aug 10 2012 *)

%o (Sage) [factorial(m) * binomial(m, 4) / 24 for m in range(4,19)] # _Zerinvary Lajos_, Jul 05 2008

%Y Cf. A053495.

%K nonn,easy

%O 4,2

%A _N. J. A. Sloane_.

%E More terms from Larry Reeves (larryr(AT)acm.org), Feb 07 2001

%E Corrected by _T. D. Noe_, Aug 10 2012

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 May 26 02:56 EDT 2020. Contains 334613 sequences. (Running on oeis4.)