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Search: id:A046968
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| A046968 |
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Numerators of coefficients in Stirling's expansion for ln Gamma(z). |
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+0
6
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| 1, -1, 1, -1, 1, -691, 1, -3617, 43867, -174611, 77683, -236364091, 657931, -3392780147, 1723168255201, -7709321041217, 151628697551, -26315271553053477373, 154210205991661, -261082718496449122051, 1520097643918070802691
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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A001067(n)=a(n) if n<574; A001067(574)=37*a(574). - Michael Somos Feb 01 2004
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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, December 1972, p. 257, Eq. 6.1.41.
L. V. Ahlfors, Complex Analysis, McGraw-Hill, 1979, p. 205
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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, December 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, December 1972, p. 257, Eq. 6.1.41.
Index entries for sequences related to Bernoulli numbers.
Eric Weisstein's World of Mathematics, Stirling's Series
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FORMULA
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From numerator 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[ Numerator[ BernoulliB[2n]/(2n(2n - 1))], {n, 1, 22}] (from Robert G. Wilson v Feb 03 2004)
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PROGRAM
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(PARI) a(n)=if(n<1, 0, numerator(bernfrac(2*n)/(2*n)/(2*n-1)))
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CROSSREFS
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Cf. A046969. Similar to but different from A001067. See A090495, A090496.
Denominators given by A046969.
Sequence in context: A060054 A120082 A120084 this_sequence A001067 A046988 A029825
Adjacent sequences: A046965 A046966 A046967 this_sequence A046969 A046970 A046971
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KEYWORD
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frac,sign,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
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