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A292830
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a(1) = 1, for n>=2, a(n) = B(2*n-1, n), where B(n, x) is the Bernoulli polynomial.
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0
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1, 3, 85, 5558, 651186, 119617025, 31697064295, 11444459810700, 5400661033684164, 3227014932144214335, 2381276769035483594793, 2126703075527239956801538, 2260781626706432961741917750, 2820945601365221814523529200893, 4082702018096881373945823658830923
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OFFSET
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1,2
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COMMENTS
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Note that B(2*n-1,n) is integer for all positive integer n, except for n=1, for which B(1,1) = 1/2, so for all n>=1, a(n) is the numerator of B(2*n-1,n). Also note that a(n) is always divisible by (2*n-1) (cf. formula).
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REFERENCES
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M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 1972, Ch. 23.
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LINKS
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FORMULA
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From [Abramowitz and Stegun] for n >= 2 we have a(n) = (2*n - 1) * (1^(2*n - 2) + 2^(2*n - 2) + ... + (n-1)^(2*n - 2)).
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MAPLE
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a := n -> `if`(n=1, 1, bernoulli(2*n-1, n)): # Peter Luschny, Sep 25 2017
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MATHEMATICA
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PROG
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(PARI) a(n) = if (n==1, 1, subst(bernpol(2*n-1), x, n)); \\ Michel Marcus, Sep 25 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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