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A187803
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E.g.f.: Sum_{n>=0} Product_{k=1..n} (1 - exp(-n*k*x)).
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1
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1, 1, 15, 829, 113487, 31137061, 15015039495, 11636995485949, 13584094722071007, 22735343245138118101, 52487807127760090483575, 162018777092079952134169069, 651747862300297714019151918927, 3344015911143306355676226376118341, 21488215819992049616143504500848490855
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OFFSET
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0,3
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COMMENTS
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Compare to the e.g.f. of A079144, enumerating certain labeled interval orders:
Sum_{n>=0} Product_{k=1..n} (1 - exp(-k*x)).
Also compare to the e.g.f. of A220181: Sum_{n>=0} (1 - exp(-n*x))^n.
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LINKS
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FORMULA
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a(n) ~ c * d^n * (n!)^3 / sqrt(n), where d = 2.426663845780394275167988381..., c = 0.504146101604802096078745... . - Vaclav Kotesovec, Nov 03 2014
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EXAMPLE
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E.g.f.: A(x) = 1 + x + 15*x^2/2! + 829*x^3/3! + 113487*x^4/4! +...
where
A(x) = 1 + (1-exp(-x)) + (1-exp(-2*1*x))*(1-exp(-2*2*x)) + (1-exp(-3*1*x))*(1-exp(-3*2*x))*(1-exp(-3*3*x)) + (1-exp(-4*1*x))*(1-exp(-4*2*x))*(1-exp(-4*3*x))*(1-exp(-4*4*x)) +...
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PROG
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(PARI) {a(n)=n!*polcoeff(sum(m=0, n, prod(k=1, m, (1-exp(-m*k*x+x*O(x^n)))) ), n)}
for(n=0, 20, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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