OFFSET
0,4
COMMENTS
a(0) = 1 as the empty product equals 1. [Joerg Arndt, Oct 06 2012]
LINKS
Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..5000 (terms 0..1000 from Alois P. Heinz)
FORMULA
G.f.: 1/(Product_{k>=0} (1-(2*k+1)*x^(2*k+1)) ). - Vladeta Jovovic, May 09 2003
From Vaclav Kotesovec, Dec 15 2015: (Start)
a(n) ~ c * 3^(n/3), where
c = 28.8343667894061364904068323836801301428320806272385991... if mod(n,3) = 0
c = 28.4762018725001067057188975211539643762050439184376103... if mod(n,3) = 1
c = 28.3618072960214990676207117911869616961300790076910101... if mod(n,3) = 2.
(End)
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1) +`if`(i>n or irem(i, 2)=0, 0, i*b(n-i, i))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..50); # Alois P. Heinz, Sep 07 2014
MATHEMATICA
b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1] + If[i>n || Mod[i, 2] == 0, 0, i*b[n-i, i]]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Apr 02 2015, after Alois P. Heinz *)
nmax = 40; CoefficientList[Series[Product[1/(1-(2*k-1)*x^(2*k-1)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Dec 15 2015 *)
PROG
(PARI)
N=66; q='q+O('q^N);
gf= 1/ prod(n=1, N, (1-(2*n-1)*q^(2*n-1)) );
Vec(gf)
/* Joerg Arndt, Oct 06 2012 */
(Maxima)
g(n):= if n=0 then 1 else if oddp(n)=true then n else 0;
P(m, n):=if n=m then g(n) else sum(g(k)*P(k, n-k), k, m, n/2)+g(n);
a(n):=P(1, n);
makelist(a(n), n, 0, 27); /* Vladimir Kruchinin, Sep 06 2014 */
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Naohiro Nomoto, Jan 29 2002
EXTENSIONS
Corrected a(0) from 0 to 1, Joerg Arndt, Oct 06 2012
STATUS
approved