This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A293113 Number T(n,k) of sets of nonempty words with a total of n letters over k-ary alphabet containing the k-th letter such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter; triangle T(n,k), n>=0, 0<=k<=n, read by rows. 14
 1, 0, 1, 0, 1, 1, 0, 2, 3, 1, 0, 2, 8, 4, 1, 0, 3, 20, 16, 5, 1, 0, 4, 47, 53, 25, 6, 1, 0, 5, 106, 173, 102, 36, 7, 1, 0, 6, 237, 532, 410, 172, 49, 8, 1, 0, 8, 522, 1615, 1545, 813, 268, 64, 9, 1, 0, 10, 1146, 4785, 5784, 3576, 1448, 394, 81, 10, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS Alois P. Heinz, Rows n = 0..40, flattened FORMULA T(n,k) = A293112(n,k) - A293112(n,k-1) for k>0, T(n,0) = A293112(n,0). EXAMPLE Triangle T(n,k) begins:   1;   0, 1;   0, 1,   1;   0, 2,   3,   1;   0, 2,   8,   4,   1;   0, 3,  20,  16,   5,   1;   0, 4,  47,  53,  25,   6,  1;   0, 5, 106, 173, 102,  36,  7, 1;   0, 6, 237, 532, 410, 172, 49, 8, 1; MAPLE h:= l-> (n-> add(i, i=l)!/mul(mul(1+l[i]-j+add(`if`(l[k]     n, 0, g(n-i, i, [l[], i])))))     end: b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,       add(b(n-i*j, i-1, k)*binomial(g(i, k, []), j), j=0..n/i)))     end: T:= (n, k)-> b(n\$2, k)-`if`(k=0, 0, b(n\$2, k-1)): seq(seq(T(n, k), k=0..n), n=0..14); MATHEMATICA h[l_] := Function[n, Total[l]!/Product[Product[1 + l[[i]] - j + Sum[If[ l[[k]] n, 0, g[n - i, i, Append[l, i]]]]]]; b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i<1, 0, Sum[b[n - i*j, i-1, k]*Binomial[g[i, k, {}], j], {j, 0, n/i}]]]; T[n_, k_] := b[n, n, k] - If[k == 0, 0, b[n, n, k - 1]]; Table[T[n, k], {n, 0, 14}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jun 04 2018, after Alois P. Heinz *) CROSSREFS Columns k=0-10 give: A000007, A000009 (for n>0), A293883, A293884, A293885, A293886, A293887, A293888, A293889, A293890, A293891. Row sums give A293114. T(2n,n) gives A293115. Cf. A182172, A293109, A293112. Sequence in context: A189117 A253580 A020921 * A154720 A071501 A004572 Adjacent sequences:  A293110 A293111 A293112 * A293114 A293115 A293116 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Sep 30 2017 STATUS approved

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

Last modified June 25 22:23 EDT 2019. Contains 324359 sequences. (Running on oeis4.)