A125179 Triangle read by rows: T(n,1) = prime(n) (the n-th prime); T(n,k) = 0 for k > n; T(n,k) = T(n-1,k) + T(n-1,k-1) for 2 <= k <= n (1 <= k <= n).

2, 3, 2, 5, 5, 2, 7, 10, 7, 2, 11, 17, 17, 9, 2, 13, 28, 34, 26, 11, 2, 17, 41, 62, 60, 37, 13, 2, 19, 58, 103, 122, 97, 50, 15, 2, 23, 77, 161, 225, 219, 147, 65, 17, 2, 29, 100, 238, 386, 444, 366, 212, 82, 19, 2, 31, 129, 338, 624, 830, 810, 578, 294, 101, 21, 2, 37, 160, 467

Offset: 1

Author

Gary W. Adamson, Nov 22 2006

Keywords

• nonn
• tabl

Comments

Sum of row n = A125180(n).

Examples

			Triangle starts:
   2;
   3,  2;
   5,  5,  2;
   7, 10,  7,  2;
  11, 17, 17,  9,  2;
  13, 28, 34, 26, 11,  2;
  17, 41, 62, 60, 37, 13,  2;
		

Crossrefs

Cf. A125180 (row sums), A007442, A254858 (rows reversed).

Cf. A007504.

Programs

Maple

T:=proc(n,k) if k=1 then ithprime(n) elif k>n then 0 else T(n-1,k)+T(n-1,k-1) fi end: for n from 1 to 12 do seq(T(n,k),k=1..n) od; # yields sequence in triangular form

Mathematica

nmax = 11;
row[1] = Prime[Range[nmax]];
row[n_] := row[n] = row[n-1] // Accumulate;
T[n_, k_] := row[n][[k]];
Table[T[n-k+1, k], {n, 1, nmax}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Oct 11 2021 *)

Formula

T(n,2) = A007504(n-1) (n>=2).

Extensions

Edited by N. J. A. Sloane, Dec 02 2006