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A266743 Irregular triangle T(n,k) read by rows: see Comments for definition. 3

%I

%S 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,

%T 60,42,10,1,2,10,15,14,5,1,12,66,110,132,66,22,1,2,12,22,33,22,11,1,

%U 420,2730,5460,10010,8580,6006,910,1

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

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

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

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

%C Prod_i (p_i)^V(n,i) / ( Prod_j (p_j)^V(k,j) * Prod_r (p_r)^U(n-k+1,r) ).

%H H. T. Davis, <a href="/A002443/a002443.pdf">Tables of the Mathematical Functions</a>, 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.

%e Triangle begins:

%e 1,

%e 1,1,

%e 2,3,1,

%e 1,2,1,

%e 6,15,10,1,

%e 2,6,5,1,

%e 12,42,42,14,1,

%e 3,12,14,7,1,

%e 10,45,60,42,10,1,

%e 2,10,15,14,5,1,

%e 12,66,110,132,66,22,1,

%e 2,12,22,33,22,11,1,

%e 420,2730,5460,10010,8580,6006,910,1,

%e ...

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

%K nonn,tabf

%O 1,4

%A _N. J. A. Sloane_, Jan 08 2016

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Last modified March 26 18:36 EDT 2019. Contains 321511 sequences. (Running on oeis4.)