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A005149
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Sequence of coefficients arising in connection with a rapidly converging series for Pi.
(Formerly M5168)
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3
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1, -24, 852, -35744, 1645794, -80415216, 4094489992, -214888573248, 11542515402255, -631467591949480, 35063515239394764, -1971043639046131296, 111949770626330347638, -6414671157989386260432, 370360217892318010055832, -21525284426246779936288192
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OFFSET
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1,2
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REFERENCES
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M. Newman and D. Shanks, On a sequence arising in series for pi, Math. Comp., 42 (1984), 199-217.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=1..16.
Index entries for sequences related to the number Pi
Index entries for reversions of series
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FORMULA
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REVERT(A014103). a(n) = -(-1)^n * A195130(n).
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EXAMPLE
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x - 24*x^2 + 852*x^3 - 35744*x^4 + 1645794*x^5 - 80415216*x^6 + 4094489992*x^7 + ...
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MATHEMATICA
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CoefficientList[InverseSeries[Series[x*Product[(1+x^k)^24, {k, 1, 16}], {x, 0, 16}], x], x] // Rest (* From Jean-François Alcover, Mar 29 2011 *)
a[ n_] := If[ n < 1, 0, SeriesCoefficient[ InverseSeries[ Series[ q Product[ 1 + q^k, {k, n}]^24, {q, 0, n}], x], {x, 0, n}]] (* Michael Somos, Sep 11 2011 *)
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PROG
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(PARI) {a(n) = if( n<1, 0, polcoeff( serreverse( x * prod( k=1, n, 1 + x^k, 1 + x * O(x^n))^24), n))}
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CROSSREFS
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Cf. A005148, A014103, A195130.
Sequence in context: A078522 A208792 A195130 * A027411 A184281 A220176
Adjacent sequences: A005146 A005147 A005148 * A005150 A005151 A005152
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KEYWORD
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sign,nice,changed
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AUTHOR
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Simon Plouffe and N. J. A. Sloane.
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EXTENSIONS
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Formula and more terms from Michael Somos, Nov 24, 2001
Signs corrected Dec 24 2001
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STATUS
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approved
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