A266743 Irregular triangle T(n,k) read by rows: see Comments for definition.

1, 1, 1, 2, 3, 1, 1, 2, 1, 6, 15, 10, 1, 2, 6, 5, 1, 12, 42, 42, 14, 1, 3, 12, 14, 7, 1, 10, 45, 60, 42, 10, 1, 2, 10, 15, 14, 5, 1, 12, 66, 110, 132, 66, 22, 1, 2, 12, 22, 33, 22, 11, 1, 420, 2730, 5460, 10010, 8580, 6006, 910, 1

Offset: 1

Author

N. J. A. Sloane, Jan 08 2016

Keywords

• nonn
• tabf

Comments

Let p_i denote the i-th prime, let pi(n) = A000720(n), and let N! = Product_{i = 1..pi(N)} (p_i)^U(N,i) be the prime factorization of N!, where U(N,i) = A115627(N,i).

Let V(n,i) = floor(n/(prime(i)-1)) = A266742(n,i).

The present triangle is defined by T(n,k) =

Product_{i} (p_i)^V(n,i) / ( Product_{j} (p_j)^V(k,j) * Product_{r} (p_r)^U(n-k+1,r) ).

Examples

			Triangle begins:
    1;
    1,    1;
    2,    3,    1;
    1,    2,    1;
    6,   15,   10,     1;
    2,    6,    5,     1;
   12,   42,   42,    14,    1;
    3,   12,   14,     7,    1;
   10,   45,   60,    42,   10,    1;
    2,   10,   15,    14,    5,    1;
   12,   66,  110,   132,   66,   22,   1;
    2,   12,   22,    33,   22,   11,   1;
  420, 2730, 5460, 10010, 8580, 6006, 910, 1;
  ...
		

Links

• H. T. Davis, Tables of the Mathematical Functions, Vols. 1 and 2, 2nd ed., 1963, Vol. 3 (with V. J. Fisher), 1962; Principia Press of Trinity Univ., San Antonio, TX. [Annotated scan of pages 204-208 of Volume 2.] See Table 3 on page 207.

Crossrefs

Cf. A000720, A002443, A002444, A115627, A266742.