%I A129273
%S A129273 1,1,2,7,26,95,344,1256,4654,17470,66234,253192,974992,3778966,14729200,
%T A129273 57683066,226806148,894791874,3540105138,14039128725,55786507642,
%U A129273 222047783006,885073034920,3532110787193,14110281656038
%V A129273 1,-1,2,-7,26,-95,344,-1256,4654,-17470,66234,-253192,974992,-3778966,
               14729200,
%W A129273 -57683066,226806148,-894791874,3540105138,-14039128725,55786507642,-222047783006,
%X A129273 885073034920,-3532110787193,14110281656038
%N A129273 G.f.: 1-q = Sum_{k>=0} a(k)*q^k * Faq(k+1,q)^2, where Faq(n,q) is the 
               q-factorial of n.
%H A129273 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               q-Factorial.html">q-Factorial</a> from MathWorld.
%F A129273 G.f.: 1-q = Sum_{k>=0} a(k)*q^k*{ Product_{i=1..k+1} (1-q^i)/(1-q) }^2.
%e A129273 Define Faq(n,q) = Product_{i=1..n} (1-q^i)/(1-q) for n>0, Faq(0,q)=1.
%e A129273 Then coefficients of q in a(k)*q^k * Faq(k+1,q)^2 begin as follows:
%e A129273 k=0: 1;
%e A129273 k=1: .. -1, -2,-1;
%e A129273 k=2: ....... 2, 8, 16,.. 20,.. 16,... 8,.... 2;
%e A129273 k=3: ......... -7,-42, -133, -294, -497,. -672, ...;
%e A129273 k=4: ............. 26,. 208,. 884, 2652,. 6266, ...;
%e A129273 k=5: .................. -95, -950,-5035,-18810, ...;
%e A129273 k=6: ........................ 344, 4128, 26144, ...;
%e A129273 k=7: ............................ -1256,-17584, ...;
%e A129273 k=8: .................................... 4654, ...;
%e A129273 Sums cancel along column j for j>1, leaving 1-q.
%o A129273 (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))}
%Y A129273 Cf. A127926.
%Y A129273 Sequence in context: A027417 A134063 A087448 this_sequence A055988 A001075 
               A113436
%Y A129273 Adjacent sequences: A129270 A129271 A129272 this_sequence A129274 A129275 
               A129276
%K A129273 sign
%O A129273 0,3
%A A129273 Paul D. Hanna (pauldhanna(AT)juno.com), Apr 07 2007