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)].

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.

Links

Table of n, a(n) for n=0..27.

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

Adjacent sequences: A141421 A141422 A141423 * A141425 A141426 A141427

Keyword

sign

Author

Paul Curtz, Aug 06 2008

Extensions

Edited by Michel Marcus, Aug 16 2013

Status

approved