A178474 Triangle T(n,m) read by rows: the denominator of the coefficient [x^m] of the inverse Euler polynomial E^{-1}(n,x), 0<=m<=n.

1, 2, 1, 2, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1

Offset

0,2

Comments

As commented in A178395, the triangle of fractions of coefficients of the inverse Euler polynomials starts in row n=0 with column 0<=m<=n as:

1;

1/2,1;

1/2,1,1;

1/2,3/2,3/2,1;

1/2,2,3,2,1;

1/2,5/2,5,5,5/2,1;

1/2,3,15/2,10,15/2,3,1;

1/2,7/2,21/2,35/2,35/2,21/2,7/2,1;

1/2,4,14,28,35,28,14,4,1;

1/2,9/2,18,42,63,63,42,18,9/2,1;

1/2,5,45/2,60,105,126,105,60,45/2,5,1;

Partial row sums (skipping the left column) in this triangle are sum_{m>=1} [x^m] E^{-1}(n,x) = 2^(n-1).

T(n,m) is the denominator of the fraction in row n and column m.

Links

Table of n, a(n) for n=0..119.

Example

1;
2,1;
2,1,1;
2,2,2,1;
2,1,1,1,1;
2,2,1,1,2,1;
2,1,2,1,2,1,1;
2,2,2,2,2,2,2,1;
2,1,1,1,1,1,1,1,1;
2,2,1,1,1,1,1,1,2,1;
2,1,2,1,1,1,1,1,2,1,1;
2,2,2,2,1,1,1,1,2,2,2,1;
2,1,1,1,2,1,1,1,2,1,1,1,1;
2,2,1,1,2,2,1,1,2,2,1,1,2,1;
2,1,2,1,2,1,2,1,2,1,2,1,2,1,1;

Mathematica

(* The function RiordanArray is defined in A256893. *)
rows = 15;
R = RiordanArray[(1 + E^#)/2&, #&, rows, True];
R // Flatten // Denominator (* Jean-François Alcover, Jul 20 2019 *)

Crossrefs

Cf. A178395 (numerators)

Sequence in context: A047895 A307322 A306737 * A164822 A361208 A110627

Adjacent sequences: A178471 A178472 A178473 * A178475 A178476 A178477

Keyword

nonn,tabl,frac

Author

Paul Curtz, May 28 2010

Status

approved