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 A115068 Triangle read by rows: T(n,k) = number of elements in the Coxeter group D_n with descent set contained in {s_k}, for 0<=k<=n-1. 7
 1, 2, 2, 4, 6, 3, 8, 16, 12, 4, 16, 40, 40, 20, 5, 32, 96, 120, 80, 30, 6, 64, 224, 336, 280, 140, 42, 7, 128, 512, 896, 896, 560, 224, 56, 8, 256, 1152, 2304, 2688, 2016, 1008, 336, 72, 9, 512, 2560, 5760, 7680, 6720, 4032, 1680, 480, 90, 10, 1024, 5632, 14080, 21120 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A115068 is the fission of the polynomial sequence (p(x,n)) by the polynomial sequence ((2x+1)^n), where p(n,x)=x^n+x^(n-1)+...+x+1, n>=0. See A193842 for the definition of fission. - Clark Kimberling, Aug 07 2011 REFERENCES A. Bjorner and F. Brenti, Combinatorics of Coxeter Groups, Springer, New York, 2005. J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge University Press, Cambridge, 1990. LINKS Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened FORMULA T(n,k)=binomial(n,k)*2^(n-k-1). T(n,1) = 2^(n-1), T(n,n) = n, for n > 1: T(n,k) = T(n-1,k-1) + 2*T(n-1,k), 1 < k < n. - Reinhard Zumkeller, Jul 22 2013 EXAMPLE First six rows: 1 2...2 4...6....3 8...16...12...4 16..40...40...20...5 32..96...120..80...30...6 MATHEMATICA z = 11; p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + 1; q[n_, x_] := (2 x + 1)^n; p1[n_, k_] := Coefficient[p[n, x], x^k]; p1[n_, 0] := p[n, x] /. x -> 0; d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}] h[n_] := CoefficientList[d[n, x], {x}] TableForm[Table[Reverse[h[n]], {n, 0, z}]] Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A115068 *) TableForm[Table[h[n], {n, 0, z}]] Flatten[Table[h[n], {n, -1, z}]]   (* A193862 *) PROG (Haskell) a115068 n k = a115068_tabl !! (n-1) !! (k-1) a115068_row n = a115068_tabl !! (n-1) a115068_tabl = iterate (\row -> zipWith (+) (row ++ [1]) \$                                 zipWith (+) (row ++ [0]) ([0] ++ row)) [1] -- Reinhard Zumkeller, Jul 22 2013 CROSSREFS Cf. A007318, A038207, A193862. Cf. A105728, A013609. Sequence in context: A260095 A209999 A127718 * A051495 A286542 A278973 Adjacent sequences:  A115065 A115066 A115067 * A115069 A115070 A115071 KEYWORD easy,nonn,tabl AUTHOR Elizabeth Morris (epmorris(AT)math.washington.edu), Mar 01 2006 STATUS approved

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Last modified March 29 03:09 EDT 2020. Contains 333104 sequences. (Running on oeis4.)