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A129716
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n! times partial sum of the sequence (1,Bernoulli numbers).
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2
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1, 2, 3, 10, 40, 196, 1176, 8352, 66816, 589248, 5892480, 67841280, 814095360, 9007096320, 126099348480, 3417110323200, 54673765171200, -1593137026252800, -28676466472550400, 6142121597716070400, 122842431954321408000, -24453765000305786880000
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = n!*(1 + Sum_{i=0..n-1} Bernoulli(i)). - R. J. Mathar, Feb 20 2008
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EXAMPLE
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The sequence of 1 followed by Bernoulli numbers is 1, 1, -1/2, 1/6,0, -1/30, 0, 1/42, .... (Cf. A027641, A027642). Its partial sums are 1, 2, 3/2, 5/3, 5/3, ... Multiplication by n! for n=0,1,2,3,... yields a(n).
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MAPLE
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MATHEMATICA
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max = 21; Accumulate[ Table[ If[n == 0, 1, BernoulliB[n-1]], {n, 0, max}]]*Range[0, max]! (* Jean-François Alcover, Mar 04 2013 *)
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PROG
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(PARI) vector(26, n, (n-1)!*(1 + sum(j=0, n-2, bernfrac(j))) ) \\ G. C. Greubel, Dec 03 2019
(Magma) [1] cat [Factorial(n)*(1 + (&+[Bernoulli(k): k in [0..n-1]]) ): n in [1..25]]; // G. C. Greubel, Dec 03 2019
(Sage) [factorial(n)*(1 + sum(bernoulli(k) for k in (0..n-1)) ) for n in (0..25)] # G. C. Greubel, Dec 03 2019
(GAP) List([0..25], n-> Factorial(n)*(1 + Sum([0..n-1], j-> Bernoulli(j)) ) ); # G. C. Greubel, Dec 03 2019
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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