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Search: id:A001812
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| A001812 |
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Coefficients of Laguerre polynomials.
(Formerly M5257 N2289)
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+0
2
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| 1, 36, 882, 18816, 381024, 7620480, 153679680, 3161410560, 66784798080, 1454424491520, 32724551059200, 761589551923200, 18341615042150400, 457129482588979200
(list; graph; listen)
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OFFSET
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5,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
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LINKS
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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
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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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PROGRAM
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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
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Sequence in context: A122038 A145150 A166790 this_sequence A075916 A062150 A011811
Adjacent sequences: A001809 A001810 A001811 this_sequence A001813 A001814 A001815
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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