OFFSET
0,3
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..420
Eric Weisstein's World of Mathematics, q-Factorial.
FORMULA
G.f.: 1-q = Sum_{k>=0} a(k)*q^k*{ Product_{i=1..k+1} (1-q^i)/(1-q) }^2.
EXAMPLE
Define Faq(n,q) = Product_{i=1..n} (1-q^i)/(1-q) for n>0, Faq(0,q)=1.
Then coefficients of q in a(k)*q^k * Faq(k+1,q)^2 begin as follows:
k=0: 1;
k=1: .. -1, -2,-1;
k=2: ....... 2, 8, 16,.. 20,.. 16,... 8,.... 2;
k=3: ......... -7,-42, -133, -294, -497,. -672, ...;
k=4: ............. 26,. 208,. 884, 2652,. 6266, ...;
k=5: .................. -95, -950,-5035,-18810, ...;
k=6: ........................ 344, 4128, 26144, ...;
k=7: ............................ -1256,-17584, ...;
k=8: .................................... 4654, ...;
Sums cancel along column j for j>1, leaving 1-q.
PROG
(PARI) {a(n)=if(n==0, 1, polcoeff(1-q- sum(k=0, n-1, a(k)*q^k*prod(j=1, k+1, (1-q^j)/ (1-q+q*O(q^(n-k))))^2), n, q))}
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Apr 07 2007
STATUS
approved