A005149 Sequence of coefficients arising in connection with a rapidly converging series for Pi. (Formerly M5168)

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).

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

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: A384172 A208792 A195130 * A027411 A184281 A220176

Adjacent sequences: A005146 A005147 A005148 * A005150 A005151 A005152

Keyword

sign,nice

Author

Simon Plouffe and N. J. A. Sloane

Extensions

Formula and more terms from Michael Somos, Nov 24 2001

Signs corrected, Dec 24 2001

Status

approved