OFFSET
0,9
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: sum(n>=0, q^(2*n+1)/prod(k=1..n, 1-q^(2*k)) * q^(2*n+1)/prod(k=1..n, 1-q^(2*k-1)) ). [Joerg Arndt, Feb 27 2014]
G.f.: x^2 * Sum_{k>=0} x^(4*k)/Product_{j=1..2*k} (1-x^j). - Seiichi Manyama, May 15 2023
MAPLE
b:= proc(n, i, t) option remember; `if`(n=0, t, `if`(i<2, 0,
b(n, i-1, t) +`if`(i>n, 0, b(n-i, i, 1-t))))
end:
a:= n-> b(n-2$2, 1):
seq(a(n), n=0..80); # Alois P. Heinz, Feb 27 2014
MATHEMATICA
b[n_, i_, t_] := b[n, i, t] = If[n==0, t, If[i<2, 0, b[n, i-1, t] + If[i>n, 0, b[n-i, i, 1-t]]]]; a[n_] := b[n-2, n-2, 1]; Table[a[n], {n, 0, 80}] (* Jean-François Alcover, Apr 08 2015, after Alois P. Heinz *)
PROG
(PARI) gf=sum(n=0, N, q^(2*n+1)/prod(k=1, n, 1-q^(2*k)) * q^(2*n+1)/prod(k=1, n, 1-q^(2*k-1)) );
concat([0], Vec(gf) ) \\ Joerg Arndt, Feb 27 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved