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A020523
a(n) = 3rd Euler polynomial evaluated at 2^n and multiplied by 4.
6
-1, 9, 161, 1665, 14849, 124929, 1024001, 8290305, 66715649, 535298049, 4288675841, 34334572545, 274777243649, 2198620602369, 17590575431681, 140731045904385, 1125874137038849, 9007096175525889, 72057181721067521, 576459103035981825, 4611679421357621249, 36893461759140036609
OFFSET
0,2
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
MAPLE
seq(euler(3, 2^i), i=0..24);
MATHEMATICA
Table[EulerE[3, 2^n], {n, 0, 40}]*4 (* Vladimir Joseph Stephan Orlovsky, Nov 03 2009 *)
PROG
(PARI) Vec(-(22*x-1)/((x-1)*(4*x-1)*(8*x-1)) + O(x^100)) \\ Colin Barker, May 04 2015
CROSSREFS
KEYWORD
sign,easy
AUTHOR
STATUS
approved