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A141424
Numerators of second column of the inverse of the triangle of polynomial coefficients P(0,x)=1, 2P(n,x)=(1+x)*[(1+x)^(n-1)+x^(n-1)].
2
1, -3, 3, -5, 5, -7, 7, 3, -3, -121, 121, 1261, -1261, -20583, 20583, 888403, -888403, -24729925, 24729925, 862992399, -862992399, -36913939769, 36913939769, 1899853421885, -1899853421885, -115841483491323, 115841483491323, 8258802033519361
OFFSET
0,2
COMMENTS
For the denominators see A053644.
The P(n,x) polynomials are based on the Euler polynomials and the inverse matrix of their coefficients is described in Example section of A133135. First column is A033999, third column is A133135.
MATHEMATICA
max = 27; p[0] = 1; p[n_] := (1+x)*((1+x)^(n-1)+x^(n-1))/2; t = Table[Coefficient[p[n], x, k], {n, 0, max+2}, {k, 0, max+2}]; a[n_] := Inverse[t][[All, 2]][[n+2]] // Numerator; Table[a[n], {n, 0, max}] (* Jean-François Alcover, Dec 16 2013 *)
PROG
(PARI) lista(n) = {m = matrix(n, n); m[1, 1] = 1; for (i=2, n, pol = (1+x)*((1+x)^(i-2)+x^(i-2))/2; for (j=1, n, m[i, j] = polcoeff(pol, j-1, x); ); ); m = 1/m; for (i=2, n, print1(numerator(m[i, 2]), ", "); ); print(); } \\ Michel Marcus, Aug 16 2013
CROSSREFS
Cf. A051717.
Sequence in context: A110560 A172170 A233808 * A069902 A335568 A085779
KEYWORD
sign
AUTHOR
Paul Curtz, Aug 06 2008
EXTENSIONS
Edited by Michel Marcus, Aug 16 2013
STATUS
approved