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A000932
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a(n) = a(n-1) + n*a(n-2); a(0) = a(1) = 1.
(Formerly M2595 N1025)
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2
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1, 1, 3, 6, 18, 48, 156, 492, 1740, 6168, 23568, 91416, 374232, 1562640, 6801888, 30241488, 139071696, 653176992, 3156467520, 15566830368, 78696180768, 405599618496, 2136915595392, 11465706820800, 62751681110208
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 20 2009: (Start)
Uses the same recursive operation as A000085.
Eigensequence of an infinite lower triangular matrix with (1, 1, 1,...)
as the main diagonal and (0, 2, 3, 4, 5,...) as the subdiagonal.
To generate A000085, replace the "0" in the subdiagonal with "1". (End)
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REFERENCES
| N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| Contribution from Paul D. Hanna, Aug 23 2011: (Start)
E.g.f. satisfies: A(x) = 1 + (1+x)*Integral A(x) dx.
E.g.f. satisfies: A(x) = A'(x)/(1+x) - (A(x)-1)/(1+x)^2.
If offset 1, then e.g.f. A(x) satisfies: F(A(x)) = 1 + x, where F(x) equals the e.g.f. of A173895 and satisfies: F'(x) = 1/(1 + x*F(x)). (End)
a(n)/a(n-1) = sqrt(n)+1/2+o(1) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jul 02 2004
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EXAMPLE
| E.g.f.: A(x) = 1 + x + 3*x^2/2! + 6*x^3/3! + 18*x^4/4! + 48*x^5/5! + 156*x^6/6! +...
If offset 1, then e.g.f. A(x) = x + x^2/2! + 3*x^3/3! + 6*x^4/4! + 18*x^5/5! + 48*x^6/6! + 156*x^7/7! +...+ a(n-1)*x^n/n! +...
satisfies F(A(x)) = 1 + x, where F(x) = e.g.f. of A173895:
F(x) = 1 + x - x^2/2! + 9*x^4/4! - 48*x^5/5! + 15*x^6/6! + 2448*x^7/7! +...
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CROSSREFS
| Cf. A173895, A000085.
Sequence in context: A108507 A083337 A019308 * A187124 A161006 A148560
Adjacent sequences: A000929 A000930 A000931 * A000933 A000934 A000935
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Jul 02 2004
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