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Search: id:A073701
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| A073701 |
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a(n) = n^2*a(n-1)+(-1)^n. |
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+0
4
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| 1, 0, 1, 8, 129, 3224, 116065, 5687184, 363979777, 29482361936, 2948236193601, 356736579425720, 51370067437303681, 8681541396904322088, 1701582113793247129249, 382855975603480604081024
(list; graph; listen)
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OFFSET
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0,4
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FORMULA
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a(n) = n!^2*Sum_{k=0..n} (-1)^k/k!^2. BesselJ(0, 2*sqrt(x))/(1-x) = Sum_{n>=0} a(n)*x^n/n!^2. a(n) = round(n!^2*BesselJ(0, 2)), n>0.
Recurrence: a(0) = 1, a(1) = 0, a(n) = (n^2-1)*a(n-1) + (n-1)^2*a(n-1), n >= 2. The sequence b(n) := n!^2 satisfies the same recurrence with the initial conditions b(0) = 1, b(1) = 1. It follows that, for n >=3, a(n) = n!^2*(1/(4 + 4/(8 + 9/(15 +...+ (n-1)^2/(n^2-1))))). Hence BesselJ(0,2) := sum {k = 0..inf} (-1)^k/k!^2 = 1/(4 + 4/(8 + 9/(15 + ...+(n-1)^2/(n^2+1 + ...)))) = 0.22388 90779 ... . Cf. A006040. - Peter Bala (pbala(AT)toucansurf.com), Jul 09 2008
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CROSSREFS
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Cf. A000166, A006040.
Cf. A006040.
Sequence in context: A027951 A041115 A041112 this_sequence A079912 A128287 A003375
Adjacent sequences: A073698 A073699 A073700 this_sequence A073702 A073703 A073704
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 30 2002
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