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 A068377 Engel expansion of sinh(1). 5
 1, 6, 20, 42, 72, 110, 156, 210, 272, 342, 420, 506, 600, 702, 812, 930, 1056, 1190, 1332, 1482, 1640, 1806, 1980, 2162, 2352, 2550, 2756, 2970, 3192, 3422, 3660, 3906, 4160, 4422, 4692, 4970, 5256, 5550, 5852, 6162, 6480, 6806, 7140, 7482, 7832, 8190 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This sequence is also the Pierce expansion of sin(1). - G. C. Greubel, Nov 14 2016 LINKS Simon Plouffe, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Engel Expansion Eric Weisstein's World of Mathematics, Hyperbolic Sine Eric Weisstein's World of Mathematics, Pierce Expansion Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = (2*n-2)*(2*n-1) = A002943(n-1) = 2*A000217(2n-2) for n>1. [Corrected and extended by M. F. Hasler, Jul 19 2015] From Colin Barker, Apr 13 2012: (Start) a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4. G.f.: x*(1 + 3*x + 5*x^2 - x^3)/(1-x)^3. (End) E.g.f.: -2 + x + 2*(1 - x + 2*x^2)*exp(x). - G. C. Greubel, Oct 27 2016 MATHEMATICA Join[{1}, Table[(2 n - 2) (2 n - 1), {n, 2, 50}]] (* Bruno Berselli, Aug 04 2015 *) LinearRecurrence[{3, -3, 1}, {1, 6, 20, 42}, 25] (* G. C. Greubel, Oct 27 2016; a(1)=1 by Georg Fischer, Apr 02 2019*) Rest@ CoefficientList[Series[x (1 + 3 x + 5 x^2 - x^3)/(1 - x)^3, {x, 0, 46}], x] (* Michael De Vlieger, Oct 28 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[Sin[1] , 7!], 50] (* G. C. Greubel, Nov 14 2016 *) PROG (PARI) A068377(n)=(n+n--)*n*2+!n \\ M. F. Hasler, Jul 19 2015 (Sage) A068377 = lambda n: rising_factorial(n*2, 2) if n>0 else 1 print [A068377(n) for n in (0..45)] # Peter Luschny, Aug 04 2015 CROSSREFS Cf. A006784, A073742 (sinh(1)). Sequence in context: A143711 A077539 A002943 * A009946 A290154 A094274 Adjacent sequences:  A068374 A068375 A068376 * A068378 A068379 A068380 KEYWORD nonn,easy AUTHOR Benoit Cloitre, Mar 03 2002 STATUS approved

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Last modified July 22 10:41 EDT 2019. Contains 325219 sequences. (Running on oeis4.)