A172528 Triangular array T(n,k) n,k>=0 is the number of k letter words formed using at most 1a,2b's,3c's,...,n#'s.

1, 1, 1, 1, 2, 3, 3, 1, 3, 8, 19, 38, 60, 60, 1, 4, 15, 53, 175, 535, 1490, 3675, 7700, 12600, 12600, 1, 5, 24, 111, 494, 2111, 8634, 33635, 123998, 428820, 1373820, 4003230, 10325700, 22522500, 37837800, 37837800

Offset: 0

Author

Geoffrey Critzer, Feb 06 2010

Keywords

• nonn
• tabf

Comments

The row lengths are n(n+1)/2 +1 (A000124).

Examples

			T(3,2) = 8 because there are 8 two letter words that can be formed using the letters a,b,b,c,c,c: {a, b}, {a, c}, {b, a}, {b, b}, {b, c}, {c, a}, {c, b}, {c, c}.
Triangle Begins
1;
1,1;
1,2,3,3;
1,3,8,19,38,60,60;
1,4,15,53,175,535,1490,3675,7700,12600,12600;
		

Crossrefs

The last entry in row n is A022915(n).

Programs

Mathematica

Table[CoefficientList[Series[Product[Sum[x^i/i!, {i, 0, n}], {n, 0, m}], {x,0, (m^2 + m)/2}], x]*Table[n!, {n, 0, (m^2 + m)/2}], {m, 0,5}] // Grid

Formula

E.g.f. for row n is Product_m=0...n[Sum_i=0...m[x^i/i! ]].