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

1,4

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) ).

Links

Table of n, a(n) for n=1..61.

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.

Example

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;
  ...

Crossrefs

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

Sequence in context: A055444 A102383 A070913 * A284050 A308644 A308184

Adjacent sequences: A266740 A266741 A266742 * A266744 A266745 A266746

Keyword

nonn,tabf

Author

N. J. A. Sloane, Jan 08 2016

Status

approved