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A118239 Engel expansion of cosh(1). 4
1, 2, 12, 30, 56, 90, 132, 182, 240, 306, 380, 462, 552, 650, 756, 870, 992, 1122, 1260, 1406, 1560, 1722, 1892, 2070, 2256, 2450, 2652, 2862, 3080, 3306, 3540, 3782, 4032, 4290, 4556, 4830, 5112, 5402, 5700, 6006, 6320, 6642, 6972, 7310, 7656, 8010, 8372 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Differs from A002939 only in first term.

This sequence is also the Pierce expansion of cos(1). - G. C. Greubel, Nov 14 2016

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Engel Expansion

Eric Weisstein's World of Mathematics, Pierce Expansion

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = A002939(n-1) = 2*(n-1)*(2*n-3) for n>1.

From Colin Barker, Apr 13 2012: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: x*(1 - x + 9*x^2 - x^3)/(1-x)^3. (End)

E.g.f.: -6 + x + 2*(3 - 3*x + 2*x^2)*exp(x). - G. C. Greubel, Oct 27 2016

MATHEMATICA

Join[{1}, Table[(2 n - 2) (2 n - 3), {n, 2, 50}]] (* Bruno Berselli, Aug 04 2015 *)

Join[{1}, LinearRecurrence[{3, -3, 1}, {2, 12, 30}, 25]] (* G. C. Greubel, Oct 27 2016 *)

PierceExp[A_, n_] := Join[Array[1 &, Floor[A]], First@Transpose@ NestList[{Floor[1/Expand[1 - #[[1]] #[[2]]]], Expand[1 - #[[1]] #[[2]]]} &, {Floor[1/(A - Floor[A])], A - Floor[A]}, n - 1]]; PierceExp[N[Cos[1] , 7!], 50] (* G. C. Greubel, Nov 14 2016 *)

PROG

(PARI) a(n)=max(4*n^2-10*n+6, 1) \\ Charles R Greathouse IV, Oct 22 2014

(Sage)

A118239 = lambda n: falling_factorial(n*2, 2) if n>0 else 1

print [A118239(n) for n in (0..46)] # Peter Luschny, Aug 04 2015

CROSSREFS

Cf. A006784, A002939, A068377.

Sequence in context: A156021 A067348 A002939 * A249055 A127118 A259127

Adjacent sequences:  A118236 A118237 A118238 * A118240 A118241 A118242

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Apr 17 2006

STATUS

approved

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Last modified July 15 16:09 EDT 2019. Contains 325049 sequences. (Running on oeis4.)