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A000575
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Tenth column of quintinomial coefficients.
(Formerly M4729 N2021)
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4
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10, 80, 365, 1246, 3535, 8800, 19855, 41470, 81367, 151580, 270270, 464100, 771290, 1245488, 1960610, 3016820, 4547840, 6729800, 9791859, 14028850, 19816225, 27627600, 38055225, 51833730, 69867525, 93262260, 123360780, 161784040, 210477476, 271763360
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OFFSET
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0,1
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COMMENTS
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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).
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REFERENCES
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L. Carlitz et al., Permutations and sequences with repetitions by number of increases, J. Combin. Theory, 1 (1966), 350-374.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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FORMULA
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a(n) = A035343(n+3, 9) = binomial(n+6, 6)*(n^3+42*n^2+677*n+5040)/(9!/6!).
G.f.: (10-20*x+15*x^2-4*x^3)/(1-x)^10; numerator polynomial is N5(9, x) from the array A063422.
a(n) = 10*C(n+3,3) + 40*C(n+3,4) + 65*C(n+3,5) + 56*C(n+3,6) + 28*C(n+3,7) + 8*C(n+3,8) + C(n+3,9) (see comment in A213887). - Vladimir Shevelev and Peter Moses, Jun 22 2012
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MATHEMATICA
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CoefficientList[Series[(10-20*x+15*x^2-4*x^3)/(1-x)^10, {x, 0, 50}], x](* Vincenzo Librandi, Mar 28 2012 *)
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CROSSREFS
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Sequence in context: A036732 A206764 A027790 * A220485 A055285 A036070
Adjacent sequences: A000572 A000573 A000574 * A000576 A000577 A000578
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Comments and more terms from Wolfdieter Lang, Aug 29 2001
More terms from Sean A. Irvine, Nov 24 2010
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STATUS
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approved
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