The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A261836 Number T(n,k) of compositions of n into distinct parts where each part i is marked with a word of length i over a k-ary alphabet whose letters appear in alphabetical order and all k letters occur at least once in the composition; triangle T(n,k), n>=0, 0<=k<=n, read by rows. 15
 1, 0, 1, 0, 1, 1, 0, 3, 10, 7, 0, 3, 15, 21, 9, 0, 5, 40, 96, 92, 31, 0, 11, 183, 832, 1562, 1305, 403, 0, 13, 266, 1539, 3908, 4955, 3090, 757, 0, 19, 549, 4281, 14791, 26765, 26523, 13671, 2873, 0, 27, 1056, 10902, 50208, 124450, 178456, 148638, 66904, 12607 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Also number of matrices with k rows of nonnegative integer entries and without zero rows or columns such that the sum of all entries is equal to n and the column sums are distinct. LINKS Alois P. Heinz, Rows n = 0..140, flattened FORMULA T(n,k) = Sum_{i=0..k} (-1)^i * C(k,i) * A261835(n,k-i). EXAMPLE T(3,2) = 10: (matrices and corresponding marked compositions are given)   [2]   [1]   [2 0]  [0 2]  [1 0]  [0 1]  [1 1]  [1 1]  [1 0]  [0 1]   [1]   [2]   [0 1]  [1 0]  [0 2]  [2 0]  [1 0]  [0 1]  [1 1]  [1 1]   3aab, 3abb, 2aa1b, 1b2aa, 1a2bb, 2bb1a, 2ab1a, 1a2ab, 2ab1b, 1b2ab. Triangle T(n,k) begins:   1;   0,  1;   0,  1,   1;   0,  3,  10,    7;   0,  3,  15,   21,     9;   0,  5,  40,   96,    92,    31;   0, 11, 183,  832,  1562,  1305,   403;   0, 13, 266, 1539,  3908,  4955,  3090,   757;   0, 19, 549, 4281, 14791, 26765, 26523, 13671, 2873; MAPLE b:= proc(n, i, p, k) option remember;       `if`(i*(i+1)/2n, 0, b(n-i, i-1, p+1, k)*binomial(i+k-1, k-1))))     end: T:= (n, k)-> add(b(n\$2, 0, k-i)*(-1)^i*binomial(k, i), i=0..k): seq(seq(T(n, k), k=0..n), n=0..12); MATHEMATICA b[n_, i_, p_, k_] := b[n, i, p, k] = If[i*(i+1)/2n, 0, b[n-i, i-1, p+1, k]*Binomial[i+k-1, k-1]]]]; T[n_, k_] := Sum[b[n, n, 0, k-i]*(-1)^i*Binomial[k, i], {i, 0, k}]; Table[ Table[T[n, k], {k, 0, n}], {n, 0, 12}] // Flatten (* Jean-François Alcover, Feb 21 2016, after Alois P. Heinz *) CROSSREFS Columns k=0-10 give: A000007, A032020 (for n>0), A261853, A261854, A261855, A261856, A261857, A261858, A261859, A261860, A261861. Main diagonal gives A032011. Row sums give A261838. T(2n,n) gives A261828. Cf. A261781, A261835. Sequence in context: A289832 A196163 A195922 * A301937 A185139 A300786 Adjacent sequences:  A261833 A261834 A261835 * A261837 A261838 A261839 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Sep 02 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 10 07:57 EDT 2022. Contains 356036 sequences. (Running on oeis4.)