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A014479
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Exponential generating function = (1+2*x)/(1-2*x)^3.
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14
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1, 8, 72, 768, 9600, 138240, 2257920, 41287680, 836075520, 18579456000, 449622835200, 11771943321600, 331576403558400, 9998303861145600, 321374052679680000, 10969567664799744000, 396275631890890752000
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: Sum_{n>=0} (2*n+1)^(n+1) * x^n / (1 + (2*n+1)*x)^(n+1). - Paul D. Hanna, Jan 02 2013
a(n) = 2^n*(n+1)^2*n!.
Recurrence: a(0) = 1, n*a(n) = 2*(n+1)^2*a(n-1). (End)
Sum_{n>=0} 1/a(n) = 2*(Ei(1/2) - gamma + log(2)), where Ei(x) is the exponential integral and gamma is Euler's constant (A001620).
Sum_{n>=0} (-1)^n/a(n) = 2*(gamma - Ei(-1/2) - gamma - log(2)). (End)
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MAPLE
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seq(add(count(Composition(k))*count(Permutation(k)), k=1..n), n=1..17); # Zerinvary Lajos, Oct 17 2006
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MATHEMATICA
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PROG
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(PARI) {a(n)=polcoeff( sum(m=0, n, (2*m+1)^(m+1)*x^m / (1 + (2*m+1)*x +x*O(x^n))^(m+1)), n)} \\ Paul D. Hanna, Jan 02 2013
for(n=0, 20, print1(a(n), ", "))
(PARI) vector(30, n, n--; n!*(n+1)^2*2^n) \\ Altug Alkan, Oct 28 2015
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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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