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Search: id:A107270
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| A107270 |
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Multiples of coefficients in asymptotic expansion of the rotational partition function for a heteronuclear diatomic molecule. |
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1
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| 1, 1, 2, 8, 72, 1440, 55008, 3507840, 342679680, 48401625600, 9472057781760, 2484361405532160, 850218223244544000, 371335242657899520000, 203148791342840318976000, 137006974339300359770112000
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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G. Herzberg, Molecular Spectra and Molecular Structure II: Infrared and Raman Spectra of Polyatomic Molecules, 1945, D. Van Nostrand, see page 505
D. A. McQuarrie, Statistical Mechanics, 2000 University Science Books, see page 100 Eq. (6-35)
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FORMULA
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Sum_{k>=0} (2k+1)exp(-x(k^2+k)) ~ (1/x)Sum_{k>=0} a(n)(2x)^n/(2n+1)!.
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EXAMPLE
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1+3exp(-2x)+5exp(-6x)+7exp(-10x)+...~1/x+1/3+(1/15)x+(4/315)x^2 +...
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PROGRAM
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(PARI) a(n)=if(n<0, 0, sum(j=0, n, bernfrac(n+j)/(n-j)!/j!)*(2*n+1)!/(-2)^n)
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CROSSREFS
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Sequence in context: A009478 A038057 A005615 this_sequence A125814 A013002 A012998
Adjacent sequences: A107267 A107268 A107269 this_sequence A107271 A107272 A107273
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, May 15 2005
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