Search: id:A033815 Results 1-1 of 1 results found. %I A033815 %S A033815 1,1,14,426,24024,2170680,287250480,52370755920,12585067447680, %T A033815 3854801333416320,1465957162768492800,677696237345719468800, %U A033815 374281829360322587827200,243388909697235614324812800,184070135024053703140543027200 %N A033815 Number of standard permutations of [ a_1..a_n b_1..b_n ] (b_i is not immediately followed by a_i, for all i). %C A033815 Also turns up as the solution to Problem #18, p. 326 of Alan Tucker's Applied Combinatorics, 4th ed, Wiley NY 2002 [Tucker's `n' is the `2n' here]. - John L Leonard, Sep 15 2003 %D A033815 Leo Chao, Paul DesJarlais and John L Leonard, A binomial identity, via derangements, Math. Gaz. 89 (2005), 268-270.. %D A033815 R. P. Stanley, Enumerative Combinatorics I, Chap.2, Exercise 10, p. 89. %H A033815 Ira Gessel, Enumerative applications of symmetric functions %F A033815 a(n)=2n(2n-1)a(n-1)+n(n-1)a(n-2); a(n)=sum(binomial(n, i)*(-1)^i*(2*n-i)!, i=0..n). %F A033815 a(n) = sum_{i=0}^n [ {nchoose i} (2n-i)! sum_{j=0}^{2n-i} (-1)^j/j! ]; also a(n) = n! sum_{i=0}^n {nchoose i} n!/(n-i)! [ sum_{j=0}^{n-i} (-1)^j {n-i choose j} (n-j)!/i! ]. - John L Leonard, Sep 15 2003 %F A033815 a(n) = Sum_{k=0..n} binomial(n,k)*A000166(n+k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 04 2006 %p A033815 A033815 := proc(n) local i; add(binomial(n, i)*(-1)^i*(2*n - i)!, i = 0 .. n) end; %Y A033815 A002119[ n ]*n!. %Y A033815 Main diagonal of array in A068106. %Y A033815 Sequence in context: A097310 A041367 A041364 this_sequence A103916 A005790 A128051 %Y A033815 Adjacent sequences: A033812 A033813 A033814 this_sequence A033816 A033817 A033818 %K A033815 nonn,easy,nice %O A033815 0,3 %A A033815 N. J. A. Sloane (njas(AT)research.att.com). Search completed in 0.001 seconds