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A282564
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Real part of A000178(n) * Sum_{k=0..n} i^k/k!, where i = sqrt(-1).
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2
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1, 1, 1, 6, 156, 18720, 13443840, 67756953600, 2732085780480000, 991419288020582400000, 3597660477435617162035200000, 143607093745702043133526671360000000, 68788027941331539080620236035063808000000000, 428344480781652673551035086691251861743206400000000000
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OFFSET
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0,4
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LINKS
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FORMULA
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a(0) = 1, a(n) = n!*a(n-1) + A000178(n-1)*cos(Pi/2*n).
Lim_{n->infinity} a(n)/G(n+2) = cos(1), where G(z) is the Barnes G-function.
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EXAMPLE
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For n = 4, a(4) = 156, which is the real part of A000178(4)*(1/0! + i/1! - 1/2! - i/3! + 1/4!) = 156+240*i.
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PROG
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(PARI) a(n) = real(prod(k=0, n, k!) * sum(k=0, n, I^k/k!));
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CROSSREFS
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The corresponding imaginary part is A282567.
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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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