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

0,7

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.

Links

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

Example

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

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}]

Crossrefs

Cf. A053644, A133135.

Sequence in context: A146583 A146458 A122573 * A136123 A045495 A045494

Adjacent sequences: A230008 A230009 A230010 * A230012 A230013 A230014

Keyword

sign,frac,easy

Author

Jean-François Alcover and Paul Curtz, Dec 20 2013

Status

approved