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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Apr 17 2006
STATUS
approved