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Search: id:A045501
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| 1, 1, 4, 14, 54, 233, 1101, 5625, 30846, 180474, 1120666, 7352471, 50772653, 367819093, 2787354668, 22039186530, 181408823710, 1551307538185, 13756835638385, 126298933271289, 1198630386463990, 11742905240821910
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OFFSET
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1,3
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COMMENT
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With leading 0 and offset 2: number of permutations beginning with 321 and avoiding 1-23. - Ralf Stephan, Apr 25 2004
Second diagonal in table of binomial recurrence coefficients. Related to A040027. - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 05 2008
Equals eigensequence of triangle A104712 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 10 2009]
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LINKS
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S. Kitaev, Generalized pattern avoidance with additional restrictions, Sem. Lothar. Combinat. B48e (2003).
S. Kitaev and T. Mansour, Simultaneous avoidance of generalized patterns.
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FORMULA
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a(n+1) = Sum_{k=0..n} binomial(n+2, k+2)*a(k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 10 2003
With offset 2, e.g.f.: x^2 + exp(exp(x))/2 * int[0..x, t^2*exp(-exp(t)+t) dt]. - Ralf Stephan, Apr 25 2004
G.f.: A(x) = Sum(x^(k+1)/((1-k*x)^2*Product(1-l*x,l=0..k)),k=0..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 05 2008
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CROSSREFS
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Cf. A045499, A045500.
A104712 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 10 2009]
Sequence in context: A118896 A145211 A060898 this_sequence A162481 A088655 A149490
Adjacent sequences: A045498 A045499 A045500 this_sequence A045502 A045503 A045504
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KEYWORD
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easy,nonn
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AUTHOR
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H. W. Gould (gould(AT)math.wvu.edu)
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 10 2003
Entry revised by N. J. A. Sloane (njas(AT)research.att.com) Dec 11 2006
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