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Search: id:A143412
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| 1, 3, 37, 743, 20841, 751019, 33065677, 1720166223, 103243039057, 7022246822099, 533794001518581, 44845718374382903, 4126339884444745657, 412678834162848948603, 44573440429472131194781
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OFFSET
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0,2
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FORMULA
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a(n) = (-1)^n*sum {k = 0..n} (-2)^k*(n+k)!/((n-k)!*k!) = (-1)^n*y_n(-4), where y_n(x) denotes the n-th Bessel polynomial. Recurrence relation: a(0) = 1, a(2) = 3, a(n) = 4*(2*n-1)*a(n-1) + a(n-2) for n >= 2. Sequence A065919(n) satisfies the same recurrence relation. Sqrt(e) = 1 + 2*sum {n = 0..inf} (-1)^n/(a(n)*a(n+1)) = 1 + 2*(1/(1*3) - 1/(3*37) + 1/(37*743) - ...).
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MAPLE
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a := n -> (-1)^n*add ((-2)^k*(n+k)!/((n-k)!*k!), k = 0..n): seq(a(n), n = 0..16);
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CROSSREFS
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Cf. A065919, A143410.
Sequence in context: A054596 A155667 A143639 this_sequence A003717 A003716 A051396
Adjacent sequences: A143409 A143410 A143411 this_sequence A143413 A143414 A143415
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KEYWORD
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easy,nonn
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AUTHOR
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Peter Bala (pbala(AT)toucansurf.com), Aug 14 2008
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