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 A229707 Triangular array read by rows.  T(n,k) is the number of strictly unimodal compositions of n with the greatest part equal to k; n>=1, 1<=k<=n. 2
 1, 0, 1, 0, 2, 1, 0, 1, 2, 1, 0, 0, 3, 2, 1, 0, 0, 4, 3, 2, 1, 0, 0, 3, 6, 3, 2, 1, 0, 0, 2, 7, 6, 3, 2, 1, 0, 0, 1, 8, 9, 6, 3, 2, 1, 0, 0, 0, 10, 12, 9, 6, 3, 2, 1, 0, 0, 0, 8, 16, 14, 9, 6, 3, 2, 1, 0, 0, 0, 7, 20, 20, 14, 9, 6, 3, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS A strictly unimodal composition is a composition such that for some j,m  1 <= x(1) < x(2) < ... < x(j) > x(j+1) > ... > x(m) >= 1. Row sums are A059618. Sum of column k is A000302(k-1). T(2*n+1,n+1) = A022567(n) for n>=0. - Alois P. Heinz, Oct 11 2013 LINKS Alois P. Heinz, Rows n = 1..141, flattened FORMULA O.g.f. for column k: x^k * prod(i=1..k-1, 1 + x^i)^2. EXAMPLE 1, 0, 1, 0, 2, 1, 0, 1, 2, 1, 0, 0, 3, 2, 1, 0, 0, 4, 3, 2, 1, 0, 0, 3, 6, 3, 2, 1, 0, 0, 2, 7, 6, 3, 2, 1, 0, 0, 1, 8, 9, 6, 3, 2, 1, 0, 0, 0, 10, 12, 9, 6, 3, 2, 1 T(7,3) = 3 because we have: 1+2+3+1 = 1+3+2+1 = 2+3+2. MAPLE b:= proc(n, t, k) option remember; `if`(n=0, `if`(k=0, 1, 0),       `if`(k>0, `if`(n b(n, 0, k): seq(seq(T(n, k), k=1..n), n=1..16);  # Alois P. Heinz, Oct 07 2013 MATHEMATICA nn=10; Table[Take[Drop[Transpose[Map[PadRight[#, nn+1, 0]&, Table[CoefficientList[Series[x^n Product[(1+x^i), {i, 1, n-1}]^2, {x, 0, nn}], x], {n, 1, nn}]]], 1][[n]], n], {n, 1, nn}]//Grid CROSSREFS Cf. A229706. Sequence in context: A170968 A114114 A090787 * A262680 A191329 A096661 Adjacent sequences:  A229704 A229705 A229706 * A229708 A229709 A229710 KEYWORD nonn,tabl AUTHOR Geoffrey Critzer, Sep 27 2013 STATUS approved

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Last modified August 22 00:43 EDT 2019. Contains 326169 sequences. (Running on oeis4.)