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 A005149 Sequence of coefficients arising in connection with a rapidly converging series for Pi. (Formerly M5168) 4
 1, -24, 852, -35744, 1645794, -80415216, 4094489992, -214888573248, 11542515402255, -631467591949480, 35063515239394764, -1971043639046131296, 111949770626330347638, -6414671157989386260432, 370360217892318010055832, -21525284426246779936288192 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Georg Fischer, Table of n, a(n) for n = 1..100 M. Newman and D. Shanks, On a sequence arising in series for pi, Math. Comp., 42 (1984), 199-217. FORMULA REVERT(A014103). a(n) = -(-1)^n * A195130(n). EXAMPLE x - 24*x^2 + 852*x^3 - 35744*x^4 + 1645794*x^5 - 80415216*x^6 + 4094489992*x^7 + ... MATHEMATICA CoefficientList[InverseSeries[Series[x*Product[(1+x^k)^24, {k, 1, 16}], {x, 0, 16}], x], x] // Rest (* 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 *) PROG (PARI) {a(n) = if( n<1, 0, polcoeff( serreverse( x * prod( k=1, n, 1 + x^k, 1 + x * O(x^n))^24), n))} CROSSREFS Cf. A005148, A014103, A195130. Sequence in context: A268632 A208792 A195130 * A027411 A184281 A220176 Adjacent sequences:  A005146 A005147 A005148 * A005150 A005151 A005152 KEYWORD sign,nice AUTHOR EXTENSIONS Formula and more terms from Michael Somos, Nov 24 2001 Signs corrected, Dec 24 2001 STATUS approved

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Last modified April 20 05:46 EDT 2021. Contains 343121 sequences. (Running on oeis4.)