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A001812
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Coefficients of Laguerre polynomials.
(Formerly M5257 N2289)
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1
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1, 36, 882, 18816, 381024, 7620480, 153679680, 3161410560, 66784798080, 1454424491520, 32724551059200, 761589551923200, 18341615042150400, 457129482588979200
(list; graph; refs; listen; history; internal format)
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OFFSET
| 5,2
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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)=-A021009(n, 5), n >= 5. a(n)=((n!/5!)^2)/(n-5)!, n >= 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-1)*f(n,5,-6), (n>=5). [From Milan R. Janjic (agnus(AT)blic.net), Mar 01 2009]
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PROG
| sage: [factorial(m)*binomial(m, 5)/120 for m in xrange (5, 23)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 05 2008
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CROSSREFS
| Sequence in context: A204101 A145150 A166790 * A169836 A075916 A062150
Adjacent sequences: A001809 A001810 A001811 * A001813 A001814 A001815
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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