A137650 Triangle read by rows, A008277 * A000012.

1, 2, 1, 5, 4, 1, 15, 14, 7, 1, 52, 51, 36, 11, 1, 203, 202, 171, 81, 16, 1, 877, 876, 813, 512, 162, 22, 1, 4140, 4139, 4012, 3046, 1345, 295, 29, 1, 21147, 21146, 20891, 17866, 10096, 3145, 499, 37, 1, 115975, 115974, 115463

Offset: 1

Author

Gary W. Adamson, Feb 01 2008

Keywords

• nonn
• tabl

Comments

Left column = Bell numbers (A000110) starting (1, 2, 5, 15, 52, 203, ...). Row sums = A005493(n+1): (1, 3, 10, 37, 151, 674, ...).

Corresponding to the generalized Stirling number triangle of first kind A049444. - Peter Luschny, Sep 18 2011

Examples

			First few rows of the triangle are
    1;
    2,   1;
    5,   4,   1;
   15,  14,   7,   1;
   52,  51,  36,  11,   1;
  203, 202, 171,  81,  16,   1;
  877, 876, 813, 512, 162,  22,   1;
  ...
		

Crossrefs

Cf. A000110, A008277, A005493, A049444.

A similar triangle is A133611.

Programs

Maple

A137650_row := proc(n) local k,i;
add(add(combinat[stirling2](n, n-i), i=0..k)*x^(n-k-1),k=0..n-1);
seq(coeff(%,x,k),k=0..n-1) end:
seq(print(A137650_row(n)),n=1..7); # Peter Luschny, Sep 18 2011

Mathematica

row[n_] := Table[StirlingS2[n, k], {k, 0, n}] // Reverse // Accumulate // Reverse // Rest;
Array[row, 10] // Flatten (* Jean-François Alcover, Dec 07 2019 *)

Formula

A008277 * A000012 as infinite lower triangular matrices. Partial sums of A008277 rows starting from the right.