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Search: id:A046969
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| A046969 |
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Denominators of coefficients in Stirling's expansion for ln Gamma(z). |
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+0
3
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| 12, 360, 1260, 1680, 1188, 360360, 156, 122400, 244188, 125400, 5796, 1506960, 300, 93960, 2492028, 505920, 396, 2418179400, 444, 21106800, 3109932, 118680, 25380, 104700960, 6468, 324360, 2283876, 382800, 40356, 201025024200, 732
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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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, p. 257, Eq. 6.1.41.
L. V. Ahlfors, Complex Analysis, McGraw-Hill, 1979, p. 205
C. Impens, Stirling's series made easy, Am. Math. Monthly, 110 (No. 8, 2003), pp. 730-735.
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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].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math.Series 55, Tenth Printing, 1972, p. 257, Eq. 6.1.41.
Thomas Bayes, A letter to to John Canton, Phil. Trans. Royal Society London, 53 (1763), 269-271.
Eric Weisstein's World of Mathematics, Stirling's Series
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FORMULA
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From denominator of Jk(z) = (-1)^(k-1)*Bk/(((2k)*(2k-1))*z^(2k-1)), so Gamma(z) = sqrt(2pi)*z^(z-0.5)*exp(-z)*exp(J(z))
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MATHEMATICA
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Table[ Denominator[ BernoulliB[2n]/(2n(2n - 1))], {n, 31}] (* Robert G. Wilson v Sep 21 2006 *)
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PROGRAM
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(PARI) a(n)=if(n<1, 0, denominator(bernfrac(2*n)/(2*n)/(2*n-1)))
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CROSSREFS
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Numerators are given in A046968.
Sequence in context: A120813 A134800 A053068 this_sequence A074094 A012553 A128043
Adjacent sequences: A046966 A046967 A046968 this_sequence A046970 A046971 A046972
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KEYWORD
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frac,nonn,nice
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AUTHOR
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Douglas Stoll, dougstoll(AT)email.msn.com
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EXTENSIONS
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More terms from Frank.Ellermann(AT)t-online.de, Jun 13 2001
Bayes reference from Henry Bottomley (se16(AT)btinternet.com), Jun 03 2003
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