A178474 - OEIS

%I #7 Jul 20 2019 08:03:57

%S 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,

%T 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,

%U 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

%N 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.

%C 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:

%C 1;

%C 1/2,1;

%C 1/2,1,1;

%C 1/2,3/2,3/2,1;

%C 1/2,2,3,2,1;

%C 1/2,5/2,5,5,5/2,1;

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

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

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

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

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

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

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

%e 1;

%e 2,1;

%e 2,1,1;

%e 2,2,2,1;

%e 2,1,1,1,1;

%e 2,2,1,1,2,1;

%e 2,1,2,1,2,1,1;

%e 2,2,2,2,2,2,2,1;

%e 2,1,1,1,1,1,1,1,1;

%e 2,2,1,1,1,1,1,1,2,1;

%e 2,1,2,1,1,1,1,1,2,1,1;

%e 2,2,2,2,1,1,1,1,2,2,2,1;

%e 2,1,1,1,2,1,1,1,2,1,1,1,1;

%e 2,2,1,1,2,2,1,1,2,2,1,1,2,1;

%e 2,1,2,1,2,1,2,1,2,1,2,1,2,1,1;

%t (* The function RiordanArray is defined in A256893. *)

%t rows = 15;

%t R = RiordanArray[(1 + E^#)/2&, #&, rows, True];

%t R // Flatten // Denominator (* _Jean-François Alcover_, Jul 20 2019 *)

%Y Cf. A178395 (numerators)

%K nonn,tabl,frac

%O 0,2

%A _Paul Curtz_, May 28 2010