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A061573
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a(n) = (n!)^2*Sum_{k=1..n} 1/k!.
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2
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1, 6, 60, 984, 24720, 890640, 43646400, 2793409920, 226266566400, 22626660268800, 2737825932441600, 394246934750592000, 66627731979077068800, 13059035467986283776000, 2938282980298221523968000, 752200442956365632925696000, 217385928014390023602954240000
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OFFSET
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1,2
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LINKS
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Harry J. Smith, Table of n, a(n) for n = 1..100
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FORMULA
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Recurrence: a(1) = 1, a(2) = 6, a(n) = n*(n+1)*a(n-1) - n*(n-1)^2*a(n-2) for n >=3. The sequence b(n) = n!^2 also satisfies this recurrence with the initial conditions b(1) = 1 and b(2) = 4. Hence we have the finite continued fraction expansion a(n)/b(n) = 1/(1-2/(6-12/(12-...-n*(n-1)^2/(n*(n+1))))). Lim_{n -> infinity} a(n)/b(n) = e - 1 = 1/(1-2/(6-12/(12-...-n*(n-1)^2/(n*(n+1))-...))) = 1/(1-1/(3-2/(4-...-n/(n+2)-...))). Cf. A000522 and A061572. - Peter Bala, Jul 10 2008
a(n) = n!*A002627(n). - R. J. Mathar, Mar 18 2017
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PROG
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(PARI) { for (n=1, 100, write("b061573.txt", n, " ", n!^2*sum(k=1, n, 1/k!)) ) } \\ Harry J. Smith, Jul 24 2009
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CROSSREFS
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Cf. A000522, A002627, A061572.
Sequence in context: A296956 A308332 A126574 * A248655 A092356 A285955
Adjacent sequences: A061570 A061571 A061572 * A061574 A061575 A061576
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, May 19 2001
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STATUS
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approved
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