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A001811
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Coefficients of Laguerre polynomials.
(Formerly M5185 N2253)
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1
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1, 25, 450, 7350, 117600, 1905120, 31752000, 548856000, 9879408000, 185513328000, 3636061228800, 74373979680000, 1586644899840000, 35272336619520000, 816302647480320000, 196456837160263680000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 4,2
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REFERENCES
| 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.
C. Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 519.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Index entries for sequences related to Laguerre polynomials
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FORMULA
| 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).
a(n)=A021009(n, 4), n >= 4. E.g.f.: x^4/(4!*(1-x)^5).
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). [From Milan R. Janjic (agnus(AT)blic.net), Mar 01 2009]
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MAPLE
| 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 (zerinvarylajos(AT)yahoo.com), Feb 07 2008
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PROG
| sage: [factorial(m)*binomial(m, 4)/24 for m in xrange (4, 19)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 05 2008
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CROSSREFS
| Cf. A053495.
Sequence in context: A018207 A001714 A016633 * A131279 A056069 A089386
Adjacent sequences: A001808 A001809 A001810 * A001812 A001813 A001814
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Feb 07 2001
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