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Search: id:A000453
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| A000453 |
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Stirling numbers of the second kind, S(n,4).
(Formerly M4722 N2018)
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+0
11
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| 1, 10, 65, 350, 1701, 7770, 34105, 145750, 611501, 2532530, 10391745, 42355950, 171798901, 694337290, 2798806985, 11259666950, 45232115901, 181509070050, 727778623825, 2916342574750, 11681056634501
(list; graph; listen)
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OFFSET
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4,2
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COMMENT
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Given a set {1,2,3,4}, a(n) is the number of occurances where the first 2 comes after the first '1', the first '3' after the first '2' and the first '4' after the first '3' in a list of n+3. For example, a(1): 1234; a(2): 11234, 12134, 12314, 12341, 12234, 12324, 12342, 12334, 12343, 12344. Related to the cereal box problem. - Kevin Nowaczyk (beakerboy99(AT)yahoo.com), Aug 02 2007
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 835.
F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 223.
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LINKS
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T. D. Noe, Table of n, a(n) for n=4..200
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 347
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FORMULA
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G.f.: x^4/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)). E.g.f. ((exp(x)-1)^4)/4!.
a(n) = (4^n-4*3^n+6*2^n-4)/24 - Kevin Nowaczyk (beakerboy99(AT)yahoo.com), Aug 02 2007
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MAPLE
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A000453:=1/(z-1)/(3*z-1)/(2*z-1)/(4*z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
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lst={}; Do[f=StirlingS2[n, 4]; AppendTo[lst, f], {n, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 27 2008]
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CROSSREFS
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Cf. A008277 (Stirling2 triangle), A016269.
Sequence in context: A022638 A003519 A056280 this_sequence A097791 A140362 A159838
Adjacent sequences: A000450 A000451 A000452 this_sequence A000454 A000455 A000456
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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