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%I #22 Nov 24 2020 17:13:55
%S 3,54,180,378,648,990,1404,1890,2448,3078,3780,4554,5400,6318,7308,
%T 8370,9504,10710,11988,13338,14760,16254,17820,19458,21168,22950,
%U 24804,26730,28728,30798,32940,35154,37440,39798,42228,44730,47304,49950
%N Engel expansion of sinh(1/3).
%C Cf. A006784 for the definition of the Engel expansion.
%C The MathWorld link mentions the closed form of the Engel expansion of sinh(1). - Georg Fischer, Nov 22 2020
%H Eric W. Weisstein, <a href="https://mathworld.wolfram.com/EngelExpansion.html">Engel Expansion</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Engel_expansion">Engel Expansion</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(1) = 3, a(n) = 18*(n*(2*n-3)+1 for n>1. - _Ralf Stephan_, Sep 03 2003
%F a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>4. G.f.: 3*x*(x^3-9*x^2-15*x-1)/(x-1)^3. - _Colin Barker_, Apr 13 2012
%e 1/3 + 1/(3*54) + 1/(3*54*180) + 1/(3*54*180*378) + 1/(3*54*180*378*648) ...
%e = 0.3395405572560086...
%e sinh(1/3) = 0.33954055725615013910126061...
%t LinearRecurrence[{3, -3, 1}, {3, 54, 180, 378}, 50]
%o (PARI) a(n)=if(n<=1, 3, 18*(n*(2*n-3)+1))
%Y Cf. A006784, A068379.
%K easy,nonn
%O 1,1
%A _Benoit Cloitre_, Mar 03 2002
%E Edited, offset 1 and a(1)=3 by _Georg Fischer_, Nov 23 2020
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