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%I #43 Aug 03 2018 04:29:35
%S 1,10,75,628,6325,75966,1063615,17017960,306323433,6126468850,
%T 134782314931,3234775558620,84104164524445,2354916606684838,
%U 70647498200545575,2260719942417458896,76864478042193603025,2767121209518969709530,105150605961720848962843,4206024238468833958514500
%N Total number of burnt pancakes flipped using the Min-bar(n) greedy algorithm.
%H Gheorghe Coserea, <a href="/A271476/b271476.txt">Table of n, a(n) for n = 1..128</a>
%H J. Sawada, A. Williams, <a href="http://www.cis.uoguelph.ca/~sawada/papers/pancake_successor.pdf">Successor rules for flipping pancakes and burnt pancakes</a>, Preprint, Theoretical Computer Science, Volume 609, Part 1, 4 January 2016, Pages 60-75.
%F a(n) = -n + 2^n * n! * Sum_{k=0..n-1} 1/(2^k*k!). (see Sawada link) - _Gheorghe Coserea_, Apr 25 2016
%F From _Altug Alkan_, Aug 01 2018: (Start)
%F a(n) = A093302(n)/2 for n >= 1.
%F a(n) = floor(e^(1/2)*n!*2^n)-n-1.
%F E.g.f.: exp(x)*(x+2*x^2)/(1-2*x). (End)
%p seq(coeff(series(factorial(n)*exp(x)*(x+2*x^2)/(1-2*x), x,n+1),x,n),n=1..20); # _Muniru A Asiru_, Aug 02 2018
%t Table[2^n*n! Sum[1/(2^k*k!), {k, 0, n - 1}] - n, {n, 20}] (* _Michael De Vlieger_, May 25 2016 *)
%o (PARI)
%o a(n) = 2^n * n! * sum(k=0, n-1, 1/(2^k*k!)) - n;
%o vector(20, n, a(n)) \\ _Gheorghe Coserea_, Apr 25 2016
%o (PARI) x='x+O('x^99); Vec(serlaplace((x+2*x^2)/(1-2*x)*exp(x))) \\ _Altug Alkan_, Aug 01 2018
%o (GAP) List([1..20],n->-n+2^n*Factorial(n)*Sum([0..n-1],k->1/(2^k*Factorial(k)))); # _Muniru A Asiru_, Aug 02 2018
%Y Cf. A019774, A093302.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Apr 09 2016
%E More terms from _Gheorghe Coserea_, Apr 25 2016
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