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A141412
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Table c(n,k) of the denominators of coefficients [x^k] P(n,x) of the polynomials P(n,x) of A129891.
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6
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1, 2, 1, 3, 1, 1, 4, 12, 2, 1, 5, 6, 4, 1, 1, 6, 180, 8, 6, 2, 1, 7, 10, 15, 2, 6, 1, 1, 8, 560, 240, 240, 6, 4, 2, 1, 9, 1260, 15120, 20, 144, 1, 12, 1, 1, 10, 12600, 672, 945, 32, 240, 8, 3, 2, 1, 11, 1260, 8400, 1512, 3024, 48, 240, 3, 1, 1, 1, 12, 166320, 100800, 64800, 12096, 12096
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Polynomials are characteristic polynomials of a particular John Couch Adams matrix.
General term: ((((-1)^(n-j))*C(j, n))*n!)*Integral (from 0 to i) (u*(u-1)*(u-2)* .. *(u-n))/(u-j)) du, i,j from 1 to n (see Flajolet et al).
Denominators are 1, 2, 12, 24, 720 =A091137
These polynomials come from the explicit case. The less interesting implicit case has same denominators (see P. Curtz 2nd reference).
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REFERENCES
| P. Flajolet, X. Gourdon, B. Salvy, Gazette des Mathematiciens 55, 1993, p.67.
P. Curtz Integration .. note 12, C.C.S.A., Arcueil 1969, p.61; ibid. pp. 62-65.
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MAPLE
| P := proc(n, x) option remember ; if n =0 then 1; else (-1)^n/(n+1)+x*add( (-1)^i/(i+1)*procname(n-1-i, x), i=0..n-1) ; expand(%) ; fi; end:
A141412 := proc(n, k) p := P(n, x) ; denom(coeftayl(p, x=0, k)) ; end: seq(seq(A141412(n, k), k=0..n), n=0..13) ; # R. J. Mathar, Aug 24 2009
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MATHEMATICA
| p[0] = 1; p[n_] := p[n] = (-1)^n/(n+1) + x*Sum[(-1)^k*p[n-1-k] / (k+1), {k, 0, n-1}];
Denominator[ Flatten[ Table[ CoefficientList[p[n], x], {n, 0, 11}]]][[1 ;; 72]]
(* From Jean-François Alcover, Jun 17 2011 *)
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CROSSREFS
| Cf. A140749 (numerators).
Sequence in context: A112543 A099478 A133913 * A178623 A160183 A168534
Adjacent sequences: A141409 A141410 A141411 * A141413 A141414 A141415
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KEYWORD
| nonn,frac,tabl,uned
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Aug 04 2008
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EXTENSIONS
| Partially edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 24 2009
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