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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
OFFSET
1,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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
KEYWORD
sign,nice
EXTENSIONS
Formula and more terms from Michael Somos, Nov 24 2001
Signs corrected, Dec 24 2001
STATUS
approved