A020523 a(n) = 3rd Euler polynomial evaluated at 2^n and multiplied by 4.
-1, 9, 161, 1665, 14849, 124929, 1024001, 8290305, 66715649, 535298049, 4288675841, 34334572545, 274777243649, 2198620602369, 17590575431681, 140731045904385, 1125874137038849, 9007096175525889, 72057181721067521, 576459103035981825, 4611679421357621249, 36893461759140036609
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (13,-44,32).
Programs
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Maple
seq(euler(3,2^i),i=0..24);
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Mathematica
Table[EulerE[3,2^n],{n,0,40}]*4 (* Vladimir Joseph Stephan Orlovsky, Nov 03 2009 *) -
PARI
Vec(-(22*x-1)/((x-1)*(4*x-1)*(8*x-1)) + O(x^100)) \\ Colin Barker, May 04 2015
Formula
a(n) = 4*8^n - 6*4^n + 1.
From Colin Barker, May 04 2015: (Start)
a(n) = 13*a(n-1) - 44*a(n-2) + 32*a(n-3) for n > 2.
G.f.: -(22*x-1)/((x-1)*(4*x-1)*(8*x-1)). (End)
E.g.f.: exp(x)*(4*exp(7*x) - 6*exp(3*x) + 1). - Elmo R. Oliveira, Feb 23 2025