The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A109876 Triangle read by rows: a(n, n) = n! and for 1 <= k < n, a(n, k) = sum_{i=0..n-1} prod_{j=i+1..i+k} f(j, n), where for x <= y, f(x, y) = x and for x > y, f(x, y) = x-y. 1

%I

%S 1,3,2,6,11,6,10,24,50,24,15,45,120,274,120,21,76,252,720,1764,720,28,

%T 119,476,1680,5040,13068,5040,36,176,828,3520,12960,40320,109584,

%U 40320,45,249,1350,6750,29880,113400,362880,1026576,362880,55,340,2090,12048

%N Triangle read by rows: a(n, n) = n! and for 1 <= k < n, a(n, k) = sum_{i=0..n-1} prod_{j=i+1..i+k} f(j, n), where for x <= y, f(x, y) = x and for x > y, f(x, y) = x-y.

%C The first four columns (excluding the initial term of each) are A000217 (triangular numbers), A006527, A062026 and A062027. The first and third diagonals are both A000142 (factorials). The second diagonal is A000254.

%C Without the exception for k = n, a(n, n) would be n*n! (A001563(n)). For example, a(3, 3) would be 1*2*3+2*3*1+3*1*2 instead of 1*2*3. The author's original description did not mention the exception. I guess it didn't make sense to him to add n identical terms. - _David Wasserman_, Oct 01 2008

%e a(5, 3) = 1*2*3 + 2*3*4 + 3*4*5 + 4*5*1 + 5*1*2 = 120.

%o (PARI) f(x, y) = if (x > y, x - y, x);

%o a(n, k) = if (n == k, n!, sum (i = 0, n - 1, prod (j = i + 1, i + k, f(j, n)))); \\ _David Wasserman_, Oct 01 2008

%Y Cf. A109877.

%K nonn,easy,tabl

%O 1,2

%A _Amarnath Murthy_, Jul 10 2005

%E Edited and extended by _David Wasserman_, Oct 01 2008

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 4 09:03 EDT 2020. Contains 336201 sequences. (Running on oeis4.)