%I A001053 M1783 N0704
%S A001053 1,0,1,2,7,30,157,972,6961,56660,516901,5225670,57999271,701216922,
%T A001053 9173819257,129134686520,1946194117057,31268240559432,533506283627401,
%U A001053 9634381345852650,183586751854827751,3681369418442407670
%N A001053 a(n+1) = n*a(n) + a(n-1) with a(0)=1, a(1)=0.
%C A001053 Denominator of continued fraction given by C(n) = [ 1; 2,3,4,...n ]. 
               - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), May 02 2001. Cf. 
               A001040.
%C A001053 If initial 1 is omitted, CONTINUANT transform of 0, 1, 2, 3, 4, 5, ...
%C A001053 Number of deco polyominoes of height n having no 1-cell columns. A deco 
               polyomino is a directed column-convex polyomino in which the height, 
               measured along the diagonal, is attained only in the last column. 
               Example: a(2)=1 because the vertical and horizontal dominoes are 
               the deco polynomioes of height 2, of which only the vertical domino 
               does not have 1-cell columns. a(n)=A121554(n,0). - Emeric Deutsch 
               (deutsch(AT)duke.poly.edu), Aug 16 2006
%D A001053 Archimedeans Problems Drive, Eureka, 20 (1957), 15.
%D A001053 E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations 
               and random generation, Theoretical Computer Science, 159, 1996, 29-42.
%D A001053 S. B. Ekhad, Problem 10356, Amer. Math. Monthly, 101 (1994), 75. [From 
               N. J. A. Sloane (njas(AT)research.att.com), Jan 29 2009]
%D A001053 M. E. Larsen, Summa Summarum, A. K. Peters, Wellesley, MA, 2007; see 
               p. 35. [From N. J. A. Sloane (njas(AT)research.att.com), Jan 29 2009]
%D A001053 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001053 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A001053 T. D. Noe, <a href="b001053.txt">Table of n, a(n) for n=0..100</a>
%H A001053 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%F A001053 a(-n) = a(n). - Michael Somos Sep 25 2005
%e A001053 a(5) = 4*a(4) + a(3) = 4*7+2 = 30.
%p A001053 a[0]:=1: a[1]:=0: for n from 2 to 23 do a[n]:=(n-1)*a[n-1]+a[n-2] od: 
               seq(a[n],n=0..23); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 
               16 2006
%t A001053 a[0] = 1; a[1] = 0; a[n_] := (n - 1)*a[n - 1] + a[n - 2]; Table[ a[n], 
               {n, 0, 21}] (from Robert G. Wilson v Feb 24 2005)
%o A001053 (PARI) a(n)=contfracpnqn(vector(abs(n),i,i))[2,2] /* Michael Somos Sep 
               25 2005 */
%Y A001053 A column of A058294.
%Y A001053 The square roots of the terms of A144656.
%Y A001053 See also the constant in A060997.
%Y A001053 Cf. A121554.
%Y A001053 Sequence in context: A154259 A066114 A088128 this_sequence A124552 A020045 
               A020135
%Y A001053 Adjacent sequences: A001050 A001051 A001052 this_sequence A001054 A001055 
               A001056
%K A001053 easy,nonn,nice,frac
%O A001053 0,4
%A A001053 N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy
%E A001053 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 19 2000