

A266743


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


3



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
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OFFSET

1,4


COMMENTS

Let p_i denote the ith 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(nk+1,r) ).


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 204208 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



KEYWORD

nonn,tabf


AUTHOR



STATUS

approved



