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

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..830

Index entries for linear recurrences with constant coefficients, signature (26,-176,256).

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)

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 *)

Prog

(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

Crossrefs

Cf. A020523 - A020526.

Sequence in context: A071606 A080282 A131931 * A157071 A174585 A186194

Adjacent sequences: A020521 A020522 A020523 * A020525 A020526 A020527

Keyword

nonn,easy

Author

Simon Plouffe

Status

approved