The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A140749 Table c(n,k) of the numerators of coefficients [x^k] P(n,x) of the polynomials P(n,x) of A129891. 6
 1, -1, 1, 1, -1, 1, -1, 11, -3, 1, 1, -5, 7, -2, 1, -1, 137, -15, 17, -5, 1, 1, -7, 29, -7, 25, -3, 1, -1, 363, -469, 967, -35, 23, -7, 1, 1, -761, 29531, -89, 1069, -9, 91, -4, 1, -1, 7129, -1303, 4523, -285, 3013, -105, 29, -9, 1, 1, -671, 16103, -7645, 31063, -781, 4781, -55, 12, -5, 1, -1, 83711, -190553 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS The polynomials P(n,x) are defined in A129891: P(0,x)=1 and P(n,x) = (-1)^n/(n+1) + x* Sum_{i=0..n-1) (-1)^i*P(n-1-i,x)/(i+1) = Sum_{k=0..n} binomial(n,k)*x^k. Numerators of A048594(n,k)/n!. - Paul Curtz, Jul 17 2008 REFERENCES P. Curtz Gazette des Mathematiciens, 1992, 52, p. 44. P. Curtz Integration Numerique .. Note 12 du Centre de Calcul Scientifique de l'Armement, Arcueil, 1969. Now in 35170, Bruz. P. Flajolet, X. Gourdon, B. Salvy id, 1993, 55, pp. 67-78. LINKS Jean-François Alcover, Plot showing roots of P(200,x) in shape of a cardioid FORMULA (n+1)*c(n,k) = (n+1-k)*c(n-1,k) - n*c(n-1, k-1). [Edgard Bavencoffe in 1992] EXAMPLE The coefficients and polynomials for n =0,1,2, ... are 1; = 1 -1/2, 1; = -1/2+x 1/3, -1, 1; = 1/3-x+x^2 -1/4, 11/12, -3/2, 1; = -1/4+11/12*x-3/2*x^2+x^3 1/5, -5/6, 7/4, -2, 1; = 1/5-5/6*x+7/4*x^2-2*x^3+x^4 -1/6, 137/180, -15/8, 17/6, -5/2, 1; = -1/6+137/180*x-15/8*x^2+17/6*x^3-5/2*x^4+x^5 1/7, -7/10, 29/15, -7/2, 25/6, -3, 1; 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: A140749 := proc(n, k) p := P(n, x) ; numer(coeftayl(p, x=0, k)) ; end: seq(seq(A140749(n, k), k=0..n), n=0..13) ; # R. J. Mathar, Aug 24 2009 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}]; Numerator[ Flatten[ Table[ CoefficientList[p[n], x], {n, 0, 11}]]][[1 ;; 69]] (* Jean-François Alcover, Jun 17 2011 *) CROSSREFS Cf. A141412 (denominators). Sequence in context: A160464 A038316 A139311 * A010188 A309389 A110089 Adjacent sequences:  A140746 A140747 A140748 * A140750 A140751 A140752 KEYWORD sign,frac,tabl AUTHOR Paul Curtz, Jul 13 2008 EXTENSIONS Edited and extended by R. J. Mathar, Aug 24 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 26 01:48 EDT 2021. Contains 346294 sequences. (Running on oeis4.)