OFFSET
0,2
REFERENCES
Richard P. Stanley, Enumerative Combinatorics, Cambridge University Press, April 1997, p. 79.
LINKS
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy] p. 825.
Fredrik Johansson, Efficient implementation of the Hardy-Ramanujan-Rademacher formula, 2012 preprint, to be published in LMS Journal of Computation and Mathematics.
Fredrik Johansson, New partition function record: p(10^20) computed (2014)
Herbert S. Wilf, Lectures on Integer Partitions
FORMULA
a(n) = (Pi*sqrt(2/3)*sqrt(10)^n-log(48)/2-n*log(10))/log(10) + O(1). - Charles R Greathouse IV, Jul 10 2012
EXAMPLE
p(10^3) = 24061467864032622473692149727991 has 32 decimal digits, so a(3) = 32.
MATHEMATICA
f[n_] := Floor[ Log[10, PartitionsP[10^n]] + 1]; Array[f, 13, 0]
PROG
(PARI) a(n)=#Str(numbpart(10^n)) \\ Charles R Greathouse IV, Jul 09 2012
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Labos Elemer, Nov 15 2002
EXTENSIONS
a(0), a(10)-a(12), a(15)=35228031 from Robert G. Wilson v, Jun 08 2010
a(13)-a(19) from Charles R Greathouse IV, Jul 09 2012 based on Johansson 2012
a(20) from Robert G. Wilson v, Mar 02 2014
STATUS
approved