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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
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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 equ. (6-35)
G. H. Wannier, Statistical Physics, Dover Publication, 1987. see page 216 equ. (11.21)
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LINKS
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Table of n, a(n) for n=0..15.
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FORMULA
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Sum_{k>=0} (2*k + 1) * exp(-x*(k^2 + k)) ~ (1/x) * Sum_{k>=0} a(k) * (2*x)^k / (2*k + 1)!.
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EXAMPLE
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1 + 3*exp(-2*x) + 5*exp(-6*x) + 7*exp(-10*x) + ... ~ 1/x + 1/3 + (1/15)*
x + (4/315)*x^2 + ...
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PROG
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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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Cf. A198954.
Sequence in context: A009478 A038057 A005615 * A125814 A013002 A012998
Adjacent sequences: A107267 A107268 A107269 * 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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STATUS
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approved
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