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A061573
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(n!)^2*Sum(1/k!,k=1..n).
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,100
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FORMULA
| 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 (pbala(AT)toucansurf.com), Jul 10 2008
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PROG
| (PARI) { for (n=1, 100, write("b061573.txt", n, " ", n!^2*sum(k=1, n, 1/k!)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 24 2009]
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CROSSREFS
| Cf. A000522, A061572.
Sequence in context: A138379 A064815 A126574 * A092356 A001416 A003267
Adjacent sequences: A061570 A061571 A061572 * A061574 A061575 A061576
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 19 2001
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