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Search: id:A055790
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| A055790 |
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a(n) = n*a(n-1) + (n-2)*a(n-2) [a(0) = 0, a(1) = 2]. |
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+0
18
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| 0, 2, 4, 14, 64, 362, 2428, 18806, 165016, 1616786, 17487988, 206918942, 2657907184, 36828901754, 547499510764, 8691268384262, 146725287298888, 2624698909845026, 49592184973992676, 986871395973226286, 20630087248996393888, 451982388752415571082
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OFFSET
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0,2
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COMMENT
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With offset 1, permanent of (0,1)-matrix of size n X (n+d) with d=1 and n-1 zeros not on a line. This is a special case of Theorem 2.3 of Seok-Zun Song et al. Extremes of permanents of (0,1)-matrices, p. 201-202. - Jaap Spies (j.spies(AT)hccnet.nl), Dec 12 2003
Number of degree-n permutations p such that p(i) != i+2 for each i=1,2,...,n. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 03 2003
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REFERENCES
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Brualdi, Richard A. and Ryser, Herbert J., Combinatorial Matrix Theory, Cambridge NY (1991), Chapter 7.
Seok-Zun Song et al., Extremes of permanents of (0,1)-matrices, Lin. Algebra and its Applic. 373 (2003), p. 197-210.
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FORMULA
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a(n) = round[(n+3+1/n)*n!/e] = 2*A000153(n) = A000255(n-1)+A000255(n) = A000166(n-1)+2*A000166(n)+A000166(n+1)
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EXAMPLE
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a(3) = 3*a(2)+(3-2)*a(1) = 12+2 = 14
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MAPLE
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f := proc(n) option remember; if n <= 1 then 2*n else n*f(n-1)+(n-2)*f(n-2); fi; end;
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CROSSREFS
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Cf. A000255, A000153, A000261, A001909, A001910, A090010, A090012-A090016.
Apart from first term, appears in triangles A047920 or A068106 of differences of factorials, i.e. as third term of A000142, A001563, A001564, A001565 etc.
Sequence in context: A046911 A089127 A132852 this_sequence A020131 A032147 A007712
Adjacent sequences: A055787 A055788 A055789 this_sequence A055791 A055792 A055793
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jul 13 2000
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