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A282567
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Imaginary part of A000178(n) * Sum_{k=0..n} i^k/k!, where i = sqrt(-1).
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2
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0, 1, 2, 10, 240, 29088, 20943360, 105529651200, 4254955536384000, 1544043321627770880000, 5603024405522854969344000000, 223654797931768113135574056960000000, 107131006056993617020920990202331136000000000, 667107003169139201955908457896071963607040000000000000
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OFFSET
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0,3
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LINKS
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FORMULA
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a(0) = 0, a(n) = n!*a(n-1) + A000178(n-1)*sin(Pi/2*n).
Lim_{n->infinity} a(n)/G(n+2) = sin(1), where G(z) is the Barnes G-function.
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EXAMPLE
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For n = 4, a(4) = 240, which is the imaginary 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) = imag(prod(k=0, n, k!) * sum(k=0, n, I^k/k!));
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CROSSREFS
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The corresponding real part is A282564.
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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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