OFFSET
0,2
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..300
J. M. Gandhi, On numbers related to partitions of a number, Amer. Math. Monthly, 76 (1969), 1033-1036.
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions.
FORMULA
G.f.: 1/(f(q)') where f(-q)=Product_{k>0} (1-q^k) is one of Ramanujan's theta functions. - Michael Somos, Apr 08 2003
a(n) ~ c * d^n, where d = -1/A143441 = 2.431619934495323994754... and c = 0.623278923942755977756856780504941340332933121682037117752100... - Vaclav Kotesovec, Jun 02 2018
EXAMPLE
G.f. = 1 + 2*x + 4*x^2 + 8*x^3 + 21*x^4 + 52*x^5 + 131*x^6 + 316*x^7 + ...
MATHEMATICA
max = 29; f[q_] := Product[1 - (-q)^k, {k, 1, max + 1}]; CoefficientList[ Series[1/f'[q], {q, 0, max}], q] (* Jean-François Alcover, Jun 18 2012, after Michael Somos *)
a[ n_] := If[ n < 0, 0, SeriesCoefficient[ 1 / D[ Normal @ Series[ QPochhammer[ -x], {x, 0, n + 1}], x], {x, 0, n}]]; (* Michael Somos, May 31 2016 *)
PROG
(PARI) {a(n) = polcoeff( 1 / eta( -x + x^2 * O(x^n))', n)};
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
Formula corrected and sequence extended by Michael Somos
STATUS
approved