Search: id:A000575
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%I A000575 M4729 N2021
%S A000575 10,80,365,1246,3535,8800,19855,41470,81367,151580,270270,464100,
%T A000575 771290,1245488,1960610,3016820,4547840,6729800,9791859,14028850,
%U A000575 19816225,27627600,38055225,51833730,69867525
%N A000575 Tenth column of quintinomial coefficients.
%C A000575 In the Carlitz et al. reference a(n)= Q_{5,n+2}(2), n >= 0, with a(n)=binomial(11+n,
               n+2)-(n+3)*binomial(n+6,n+2), (eq.(3.3), p. 356, with n=5, m->n+2,
               r=2). Q_{5,m}(2) is the number of sequences (i_1,i_2,...,i_m) with 
               i_s, s=1,...,m, from {1,2,3,4,5} (repetitions allowed), with exactly 
               2 increases between successive elements (first position is counted 
               as an increase).
%D A000575 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000575 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000575 L. Carlitz et al., Permutations and sequences with repetions by number 
               of increases, J. Combin. Theory, 1 (1966), 350-374.
%F A000575 a(n)= A035343(n+3, 9)=binomial(n+6, 6)*(n^3+42*n^2+677*n+5040)/(9!/6!).
%F A000575 G.f.: (10-20*x+15*x^2-4*x^3)/(1-x)^10; numerator polynomial is N5(9, 
               x) from the array A063422.
%Y A000575 Sequence in context: A077245 A036732 A027790 this_sequence A055285 A036070 
               A125373
%Y A000575 Adjacent sequences: A000572 A000573 A000574 this_sequence A000576 A000577 
               A000578
%K A000575 nonn
%O A000575 0,1
%A A000575 N. J. A. Sloane (njas(AT)research.att.com).
%E A000575 Comments and more terms from Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), 
               Aug 29 2001

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