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Search: id:A129273
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| A129273 |
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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. |
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+0
9
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| 1, -1, 2, -7, 26, -95, 344, -1256, 4654, -17470, 66234, -253192, 974992, -3778966, 14729200, -57683066, 226806148, -894791874, 3540105138, -14039128725, 55786507642, -222047783006, 885073034920, -3532110787193, 14110281656038
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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Eric Weisstein's World of Mathematics, q-Factorial from MathWorld.
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FORMULA
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G.f.: 1-q = Sum_{k>=0} a(k)*q^k*{ Product_{i=1..k+1} (1-q^i)/(1-q) }^2.
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EXAMPLE
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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.
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PROGRAM
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(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))}
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CROSSREFS
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Cf. A127926.
Sequence in context: A027417 A134063 A087448 this_sequence A055988 A001075 A113436
Adjacent sequences: A129270 A129271 A129272 this_sequence A129274 A129275 A129276
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KEYWORD
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sign
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Apr 07 2007
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