A020524 a(n) = 4th Euler polynomial evaluated at 2^n.
0, 2, 132, 3080, 57360, 983072, 16252992, 264241280, 4261413120, 68451041792, 1097364145152, 17575006177280, 281337537761280, 4502500115750912, 72048797944922112, 1152851135862702080, 18446181123756195840, 295143401579725586432, 4722330454072626511872, 75557575495538172231680
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..830
- Index entries for linear recurrences with constant coefficients, signature (26,-176,256).
Programs
-
Maple
seq(euler(4, 2^n), n=0..24);
-
Mathematica
Table[EulerE[4,2^n],{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Nov 03 2009 *) -
PARI
concat(0, Vec(-2*x*(40*x+1)/((2*x-1)*(8*x-1)*(16*x-1)) + O(x^100))) \\ Colin Barker, May 04 2015
Formula
From Colin Barker, May 04 2015: (Start)
a(n) = 2^n - 2^(1+3*n) + 16^n.
a(n) = 26*a(n-1) - 176*a(n-2) + 256*a(n-3) for n > 2.
G.f.: -2*x*(40*x+1)/((2*x-1)*(8*x-1)*(16*x-1)). (End)
E.g.f.: exp(2*x)*(exp(14*x) - 2*exp(6*x) + 1). - Elmo R. Oliveira, Feb 22 2025