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A001475
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a(n) = a(n-1) + n a(n-2).
(Formerly M1449 N0573)
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2
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1, 2, 5, 13, 38, 116, 382, 1310, 4748, 17848, 70076, 284252, 1195240, 5174768, 23103368, 105899656, 498656912, 2404850720, 11879332048, 59976346448, 309442319456, 1628921941312, 8746095288800, 47840221880288, 266492604100288, 1510338372987776
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OFFSET
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1,2
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COMMENTS
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a(n) = number of partitions of [n] in which the block containing 1 is of length <= 3 and all other blocks are of length <= 2. Example: a(4)=13 counts all 15 partitions of [4] except 1234 and 1/234. - David Callan, Jul 22 2008
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 86 (divided by 2).
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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LINKS
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Table of n, a(n) for n=1..26.
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FORMULA
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E.g.f.: 1/2*(1+x)*exp(x+1/2*x^2)-1/2. - Vladeta Jovovic, Nov 04 2003
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MATHEMATICA
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RecurrenceTable[{a[1]==1, a[2]==2, a[n]==a[n-1]+n a[n-2]}, a, {n, 30}] (* From Harvey P. Dale, Apr 21 2012 *)
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CROSSREFS
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Equals (1/2) A000085(n+1). Cf. A001189, A013989.
Sequence in context: A064384 A148302 A149857 * A149858 A148303 A148304
Adjacent sequences: A001472 A001473 A001474 * A001476 A001477 A001478
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Harvey P. Dale, Apr 21 2012
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STATUS
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approved
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