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 A127926 G.f.: 1-q = Sum_{k>=0} a(k)*q^k*Faq(k+1,q), where Faq(n,q) is the q-factorial of n. 2
 1, -1, 1, -2, 4, -7, 11, -18, 35, -76, 166, -358, 775, -1686, 3638, -7716, 16108, -33349, 69022, -143605, 301179, -636932, 1355855, -2896168, 6186750, -13183426, 27988755, -59197443, 124824911, -262699256, 552438175, -1162010894, 2446434685, -5156873960 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS FORMULA G.f.: 1-q = Sum_{k>=0} a(k)*q^k*Product_{i=1..k+1} (1-q^i)/(1-q). 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) begin as follows: k=0: 1; k=1: .. -1, -1; k=2: ....... 1, 2, 2,. 1; k=3: ......... -2,-6,-10,-12,-10,. -6,. -2; k=4: ............. 4, 16, 36, 60,. 80,. 88,.. 80, ...; k=5: ................ -7,-35,-98,-203,-343, -497, ...; k=6: .................... 11, 66, 220, 539, 1078, ...; k=7: ....................... -18,-126,-486,-1368, ...; k=8: ............................. 35, 280, 1225, ...; k=9: ................................. -76, -684, ...; k=10: ...................................... 166, ...; Sums cancel down 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))))), n, q))} CROSSREFS First column of A179750. [From Mats Granvik, Jul 26 2010] Sequence in context: A239552 A023426 A157134 * A078513 A308871 A325546 Adjacent sequences:  A127923 A127924 A127925 * A127927 A127928 A127929 KEYWORD sign AUTHOR Paul D. Hanna, Feb 06 2007 STATUS approved

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Last modified September 21 05:55 EDT 2020. Contains 337267 sequences. (Running on oeis4.)