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A271476
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Total number of burnt pancakes flipped using the Min-bar(n) greedy algorithm.
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2
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1, 10, 75, 628, 6325, 75966, 1063615, 17017960, 306323433, 6126468850, 134782314931, 3234775558620, 84104164524445, 2354916606684838, 70647498200545575, 2260719942417458896, 76864478042193603025, 2767121209518969709530, 105150605961720848962843, 4206024238468833958514500
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = -n + 2^n * n! * Sum_{k=0..n-1} 1/(2^k*k!). (see Sawada link) - Gheorghe Coserea, Apr 25 2016
a(n) = floor(e^(1/2)*n!*2^n)-n-1.
E.g.f.: exp(x)*(x+2*x^2)/(1-2*x). (End)
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MAPLE
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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
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MATHEMATICA
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Table[2^n*n! Sum[1/(2^k*k!), {k, 0, n - 1}] - n, {n, 20}] (* Michael De Vlieger, May 25 2016 *)
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PROG
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(PARI)
a(n) = 2^n * n! * sum(k=0, n-1, 1/(2^k*k!)) - n;
(PARI) x='x+O('x^99); Vec(serlaplace((x+2*x^2)/(1-2*x)*exp(x))) \\ Altug Alkan, Aug 01 2018
(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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