A230011 Numerators of sum of rows of the inverse of the triangle of Euler polynomial coefficients P(0,x)=1, 2P(n,x)=(1+x)*[(1+x)^(n-1)+x^(n-1)].

1, 0, 1, -1, 1, -1, 3, -3, -11, 11, 113, -113, -1269, 1269, 20575, -20575, -888419, 888419, 24729909, -24729909, -862992415, 862992415, 36913939753, -36913939753, -1899853421901, 1899853421901, 115841483491307, -115841483491307

Offset: 0

Author

Jean-François Alcover and Paul Curtz, Dec 20 2013

Keywords

• sign
• frac
• easy

Comments

See A133135.

Denominators are 1, 1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 32, 32, ..., a sequence which matches A053644, except the first term.

Examples

			1, 0, 1/2, -1/2, 1/4, -1/4, 3/4, -3/4, -11/8, 11/8, 113/8, -113/8, ...
		

Crossrefs

Cf. A053644, A133135.

Programs

Mathematica

max = 30; p[0, ] = 1; p[n, x_] := (1+x)*((1+x)^(n-1)+x^(n-1))/2; t = Total /@ Inverse @ Table[Coefficient[p[n, x], x, k], {n, 0, max+2}, {k, 0, max+2}]; a[n_] := t[[n+1]] // Numerator; Table[a[n], {n, 0, max}]