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Search: id:A088801
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| A088801 |
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Numerators of coefficients of powers of n^(-1) in the Romanovsky series expansion of the mean of the standard deviation from a normal population. |
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+0
2
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| 1, -3, -7, -9, 59, 483, -2323, -42801, 923923, 30055311, -170042041, -8639161167, 99976667055, 7336972779615, -42962450319915, -4309733345367105, 203289825295660035, 26751125064470578695, -158415664732997134045, -26488943422458070446915
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Asymptotic expansion of Gamma(N/2) / Gamma((N-1)/2) = (N/2)^(1/2) * (c(0) + c(1)/N + c(2)/N^2 + ... ). a(n) = numerator(c(n)). - Michael Somos Aug 23 2007
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LINKS
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Eric Weisstein's World of Mathematics, Standard Deviation Distribution
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PROGRAM
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(PARI) {a(n) = local(A); if(n < 0, 0, A = 1 + O(x) ; for( k = 1, n, A = truncate(A) + x^2 * O(x^k); A += x^k/4/k * polcoeff( subst( A, x, x/(1+2*x))^2 - A^2/(1-x)^2/(1+2*x), k+1 ) ); numerator( polcoeff( A, n ) ) ) } /* Michael Somos Aug 23 2007 */
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CROSSREFS
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Cf. A088802.
Sequence in context: A033681 A074339 A115164 this_sequence A003033 A087147 A103115
Adjacent sequences: A088798 A088799 A088800 this_sequence A088802 A088803 A088804
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KEYWORD
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sign,frac
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Oct 16, 2003
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