A005149 Sequence of coefficients arising in connection with a rapidly converging series for Pi.

1, -24, 852, -35744, 1645794, -80415216, 4094489992, -214888573248, 11542515402255, -631467591949480, 35063515239394764, -1971043639046131296, 111949770626330347638, -6414671157989386260432, 370360217892318010055832, -21525284426246779936288192

Offset: 1

Author

Simon Plouffe and N. J. A. Sloane

Keywords

• sign
• nice

Examples

			x - 24*x^2 + 852*x^3 - 35744*x^4 + 1645794*x^5 - 80415216*x^6 + 4094489992*x^7 + ...
		

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.
• Index entries for sequences related to the number Pi
• Index entries for reversions of series

Crossrefs

Cf. A005148, A014103, A195130.

Programs

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 *)

PARI

{a(n) = if( n<1, 0, polcoeff( serreverse( x * prod( k=1, n, 1 + x^k, 1 + x * O(x^n))^24), n))}

Formula

REVERT(A014103). a(n) = -(-1)^n * A195130(n).

Extensions

Formula and more terms from Michael Somos, Nov 24 2001

Signs corrected, Dec 24 2001